Artikel ini memberikan latihan soal sekaligus pembahasan Penilaian Tengah Semester 2019 mata pelajaran Matematika IPA kelas XII
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Tak terasa, kamu sudah berada di pertengahan semester ganjil tahun ajaran 2019/2020. Penilaian Tengah Semester (PTS) pun tinggal menghitung hari. Kamu sudah menyiapakan apa saja nih? Apalagi untuk kamu yang duduk di bangku kelas XII. Nilai kamu di PTS ini sangat penting untuk menghadapi SNMPTN sekaligus bisa menjadi persiapan untuk kamu menghadapi ujian-ujian selanjutnya. Ayo, persiapkan diri hadapi PTS dengan latihan soal Matematika IPA kelas XII berikut ini.
Baca juga: Latihan dan Pembahasan Soal UTS Fisika SMA Kelas 12
TOPIK: BIDANG DATAR
SUBTOPIK: DALIL PROYEKSI & DALIL STEWART
- Perhatikan gambar bangun datar di bawah ini!
Jika panjang PQ = PS = 4 dm dan QR = 6 dm maka SR = ….
- 5 dm
- 6 dm
- 7 dm
- 8 dm
- 10 dm
Jawaban B
Pembahasan :
Gunakan dalil proyeksi untuk menyelesaikan soal di atas.
Maka,
Karena PR menyatakan panjang sisi segitiga maka nilai PR yang memenuhi adalah 10.
Sehingga diperoleh SR = PR – PS = 10 dm – 4 dm = 6 dm.
TOPIK: BIDANG DATAR
SUBTOPIK: GARIS ISTIMEWA SEGITIGA II
2. Perhatikan gambar di bawah ini.
Diketahui garis CD adalah garis bagi segitiga ABC. Panjang CD adalah ….
Jawaban B
Pembahasan :
Karena CD adalah garis bagi segitiga ABC, maka
Misalkan
Karena AB = 14 cm, maka
Sehingga BD = 10 cm dan AD =
Karena CD adalah garis bagi segitiga ABC, maka
Karena panjang sisi tidak mungkin negatif maka
TOPIK: BIDANG RUANG (KEDUDUKAN DAN PROYEKSI)
SUBTOPIK: KEDUDUKAN TITIK
3. Perhatikan kubus ABCD.EFGH di bawah ini.
Jika titik P, Q dan R berturut-turut terletak pada rusuk BF, AE dan BC maka pernyataan yang benar adalah ….
- Titik P berada pada bidang CDG
- Titik Q berada pada bidang ABCD
- Titik Q dan R sebidang
- Titik R berada pada bidang ABD
- Titik P, Q dan R sebidang
Jawaban D
Pembahasan :
- Titik P terletak pada bidang ABFE dan bidang BCGF
- Titik Q terletak pada bidang ABFE dan bidang ADHE
- Titik R terletak pada bidang ABCD dan bidang BCGF
- Titik P dan Q sebidang (pada bidang ABFE)
- Titik P dan R sebidang (pada bidang BCGF)
Jadi dari beberapa pernyataan di atas maka pernyataan yang benar pada pilihan jawaban adalah titik R berada pada bidang ABD, karena jika bidang ABD diperluas maka diperoleh bidang ABCD.
TOPIK: BIDANG RUANG (KEDUDUKAN DAN PROYEKSI)
SUBTOPIK: KEDUDUKAN GARIS TERHADAP BIDANG
- Perhatikan kubus ABCD.EFGH di bawah ini.
Misalkan P adalah titik tengah ED. Bidang yang tegak lurus dengan garis AP adalah bidang ….
- BCHE
- ADGF
- CDEF
- BDHF
- ABGH
Jawaban C
Pembahasan :
Perhatikan bahwa karena P adalah titik tengah dari diagonal ED maka P juga menjadi titik tengah dari diagonal AH.
Garis AP dapat diperpanjangan menjadi garis AH.
Garis AP dan bidang BCHE
Perhatikan bahwa garis EF terletak pada bidang BCHE. Namun, garis AP tidak tegak lurus garis EH. Sehingga AP tidak tegak lurus bidang BCHE.
Garis AP dengan bidang ADGF
Perhatikan bahwa garis AD terletak pada bidang ADGF. Namun, garis AP tidak tegak lurus dengan garis AD. Sehingga AP tidak tegak lurus bidang ADGF.
Garis AP dan bidang CDEF
Perhatikan gambar di bawah ini.
Perhatikan bahwa AH tegak lurus ED maka AP juga tegak lurus ED. Bidang yang memuat ED adalah bidang CDEF. Sehingga garis AP tegak lurus bidang CDEF.
Garis AP dan bidang BDHF
Perhatikan bahwa garis DH berada pada bidang BDHF. Namun, garis AH (sebagai perpanjangan garis AP) tidak tegak lurus garis DH. Sehingga AP tidak tegak lurus bidang BDHF.
Garis AP dan bidang ABGH
Garis AP tidak tegak lurus bidang ABGH karena gari AP terletak pada bidang ABGH.
TOPIK: BIDANG RUANG (KEDUDUKAN DAN PROYEKSI)
SUBTOPIK: PROYEKSI
5. Perhatikan kubus ABCD.EFGH berikut ini.
Proyeksi bidang BFC ke bidang CHE adalah bidang….
- BCE
- BCD
- BCM dengan M titik tengan BE
- BCN dengan N titik tengah CH
- BCO dengan O titik tengah EH
Jawaban C
Pembahasan :
Perhatikan gambar di bawah ini.
Bidang BFC jika diperluas maka akan menjadi bidang BCHE. Garis potong bidang BCHE dengan bidang BCE adalah garis BC. Kemudian proyeksikan titik F ke bidang BCHE.
Misalkan titik M adalah titik potong diagonal sisi BE dan diagonal sisi AF. Maka titik M berada tepat pada pertengahan garis BE.
Ingat kembali bahwa diagonal sisi pada kubus saling tegak lurus. Sehingga, proyeksi titik F ke bidang BCHE sama dengan proyeksi titik F ke garis BE, yaitu titik M.
Jadi proyeksi bidang BCF ke bidang BCHE adalah bidang BCM dimana M adalah titik tengah BE.
TOPIK: BIDANG RUANG (JARAK)
SUBTOPIK: JARAK TITIK KE BIDANG
6. Diketahui sebuah kubus ABCD.EFGH dengan rusuk 6 cm. Jarak titik E ke bidang ACH adalah …. cm.
JAWABAN : B
PEMBAHASAN :
Jika kita tambahkan satu buah kubus lagi disebelah kiri kubus ABCD.EFGH kemudian perluas bidang ACH seperti pada gambar berikut ini.
Sehingga jarak titik E ke bidang ACH sama dengan jarak titik E ke garis AP’, atau sama juga dengan jarak titik D ke titik O.
Sehingga dengan persamaan luas segitiga DHP diperoleh :
Jadi Jarak titik E ke bidang ACH adalah
TOPIK: BIDANG RUANG (JARAK)
SUBTOPIK: JARAK DUA BIDANG SEJAJAR
7. Diketahui kubus ABCD.EFGH dengan panjang rusuk 10 cm. Jarak bidang ACH dengan bidang BEG adalah …. cm
JAWABAN : A
PEMBAHASAN :
Untuk memudahkan buat bidang diagonal BDHF dengan titik M dan titik N adalah titik tengah perpotongan diagonal atap dan alas seperti gambar berikut.
Bidang BEG berptongan dengan bidang BDHF di garis BM. Sedangkan bidang ACH berpotongan dengan bidang BDHF di garis HN.
Jika kita buat segitiga BMN pada bidang diagonal BDHF maka jarak bidang ACH ke bidang BEG sama dengan jarak titik N ke garis BM atau sama dengan NO.
Dengan persamaan luas segitiga BMN maka diperoleh :
Jadi jarak bidang ACH ke bidang BEG adalah
TOPIK: BIDANG RUANG (SUDUT)
SUBTOPIK: SUDUT DUA GARIS
8. Diketahui kubus ABCH.EFGH dengan rusuk 4 cm. Titik T membagi dua rusuk BC menjadi dua bagian. Jika adalah sudut antara garis HT dengan garis BG maka
Jawaban C
Pembahasan :
Perhatikan kubus di bawah :
Kemudian pada segitiga ATH, misalkan R adalah titik pada AH sehingga garis TR tegak lurus garis AH.
Dengan aturan cos maka diperoleh,
Kemudian hitung nilai sin dengan rumus identitas trigonometri berikut :
Jadi nilai dari
TOPIK: BIDANG RUANG (SUDUT)
SUBTOPIK: SUDUT GARIS DAN BIDANG
9. Diketahui sebuah kubus ABCD.EFGH dengan panjang sisi kubus . Sinus sudut antara rusuk BF ke bidang BEG adalah….
Jawaban B
Pembahasan :
Perhatikan gambar di bawah ini.
Diketahui :
Sehingga,
Maka,
Sinus sudut antara rusuk BF ke bidang BEG adalah
TOPIK: BIDANG RUANG (SUDUT)
SUBTOPIK: IRISAN BIDANG
10. Diketahui kubus ABCD.EFGH dengan titik M adalah titik tengah rusuk CG. Irisan bidang yang melalu titik M, D dan F adalah ….
- Segitiga
- Segitiga sama sisi
- Segiempat
- Segilima
- Persegi
Jawaban C
Pembahasan :
Perhatikan gambar di bawah ini.
Karena titik D terletak pada rusuk yang bersebrangan dengan titik F maka titik M akan berseberangan pula dengan titik lain di rusuk AE. Misalkan titik N adalah titik tengah rusuk AE.
Sehingga bidang yang terbentuk adalah bidang segiempat NDFM seperti pada gambar di atas.
Gimana, membantu ‘kan? Mau latihan lebih banyak soal? Yuk, latihan soal-soal terkait materi ujian sekolah di ruangbelajar.
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<h1 class="content-title">
Latihan Soal Penilaian Tengah Semester 2019: Matematika IPA Kelas XII </h1>
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<p class="content-author"><a href="https://www.ruangguru.com/blog/author/shabrina-alfari" class="">Shabrina Alfari</a> </p>
<p class="content-info"><span>September 17, 2019 • </span> <span>6 minutes read</span></p>
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<p style="text-align: justify;"><em><img decoding="async" style="width: 820px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/UN_-_Latihan_soal_Penilaian_Tengah_Semester_Matematika_Saintek_kelas_12-01.png" alt="Latihan Soal Penilaian Tengah Semester 2019: Matematika IPA Kelas XII" width="820" /></em></p>
<p><span id="more-7804"></span></p>
<p style="text-align: justify;"><em>Artikel ini memberikan latihan soal sekaligus pembahasan Penilaian Tengah Semester 2019 mata pelajaran Matematika IPA kelas XII</em></p>
<p style="text-align: center;">—</p>
<p style="text-align: justify;">Tak terasa, kamu sudah berada di pertengahan semester ganjil tahun ajaran 2019/2020. Penilaian Tengah Semester (PTS) pun tinggal menghitung hari. Kamu sudah menyiapakan apa saja <em>nih</em>? Apalagi untuk kamu yang duduk di bangku kelas XII. Nilai kamu di PTS ini sangat penting untuk menghadapi SNMPTN sekaligus bisa menjadi persiapan untuk kamu menghadapi ujian-ujian selanjutnya. Ayo, persiapkan diri hadapi PTS dengan latihan soal Matematika IPA kelas XII berikut ini.</p>
<p style="text-align: justify;"><strong><span style="color: #990100;">Baca juga:</span> <a href="/latihan-dan-pembahasan-soal-uts-fisika-sma-kelas-12" rel=" noopener">Latihan dan Pembahasan Soal UTS Fisika SMA Kelas 12</a></strong></p>
<p style="text-align: justify;"><img decoding="async" style="width: 820px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Untitled%20design%20(1)-24.png" alt="Untitled design (1)-24" width="820" /></p>
<p style="text-align: justify;"><strong>TOPIK: BIDANG DATAR</strong></p>
<p style="text-align: justify;"><strong>SUBTOPIK: DALIL PROYEKSI & DALIL STEWART</strong></p>
<ol style="text-align: justify;">
<li>Perhatikan gambar bangun datar di bawah ini!</li>
</ol>
<p style="text-align: justify;"><img decoding="async" style="width: 286px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/2-92.png" alt="2-92" width="286" /></p>
<p style="text-align: justify;">Jika panjang PQ = PS = 4 dm dan QR = 6 dm maka SR = ….</p>
<ol style="list-style-type: upper-alpha; text-align: justify;">
<li>5 dm</li>
<li>6 dm</li>
<li>7 dm</li>
<li>8 dm</li>
<li>10 dm</li>
</ol>
<p style="text-align: justify;"><strong>Jawaban B</strong></p>
<p style="text-align: justify;"><strong>Pembahasan :</strong></p>
<p style="text-align: justify;">Gunakan dalil proyeksi untuk menyelesaikan soal di atas.</p>
<p style="text-align: justify;">Maka,</p>
<p style="text-align: justify;"><img decoding="async" style="width: 162px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/1-405577069094.png" alt="1-405577069094" width="162" /></p>
<p style="text-align: justify;">Karena PR menyatakan panjang sisi segitiga maka nilai PR yang memenuhi adalah 10.</p>
<p style="text-align: justify;">Sehingga diperoleh SR = PR – PS = 10 dm – 4 dm = 6 dm.</p>
<p><img decoding="async" style="width: 820px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Untitled%20design%20(1)-24.png" alt="Untitled design (1)-24" width="820" /></p>
<p style="text-align: justify;"><strong>TOPIK: BIDANG DATAR</strong></p>
<p style="text-align: justify;"><strong>SUBTOPIK: GARIS ISTIMEWA SEGITIGA II</strong></p>
<p style="text-align: justify;">2. Perhatikan gambar di bawah ini.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 323px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/3-55.png" alt="3-55" width="323" /></p>
<p style="text-align: justify;">Diketahui garis CD adalah garis bagi segitiga ABC. Panjang CD adalah ….</p>
<p><img decoding="async" style="width: 61px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/4-25.png" alt="4-25" width="61" /></p>
<p style="text-align: justify;"><strong>Jawaban B</strong></p>
<p style="text-align: justify;"><strong>Pembahasan :</strong></p>
<p style="text-align: justify;">Karena CD adalah garis bagi segitiga ABC, maka</p>
<p style="text-align: justify;"><img decoding="async" style="width: 76px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/5-26.png" alt="5-26" width="76" /></p>
<p style="text-align: justify;">Misalkan <img decoding="async" style="width: 147px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/6-23.png" alt="6-23" width="147" /></p>
<p style="text-align: justify;">Karena AB = 14 cm, maka</p>
<p style="text-align: justify;"> <img decoding="async" style="width: 105px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/7-22.png" alt="7-22" width="105" /></p>
<p style="text-align: justify;">Sehingga BD = 10 cm dan AD = <img decoding="async" style="width: 94px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/8-22.png" alt="8-22" width="94" /></p>
<p style="text-align: justify;">Karena CD adalah garis bagi segitiga ABC, maka</p>
<p style="text-align: justify;"><img decoding="async" style="width: 177px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/9-26.png" alt="9-26" width="177" /></p>
<p style="text-align: justify;">Karena panjang sisi tidak mungkin negatif maka <img decoding="async" style="width: 101px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/10-20.png" alt="10-20" width="101" /></p>
<p style="text-align: justify;"><img decoding="async" style="width: 820px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Untitled%20design%20(1)-24.png" alt="Untitled design (1)-24" width="820" /></p>
<p style="text-align: justify;"><strong>TOPIK: BIDANG RUANG (KEDUDUKAN DAN PROYEKSI)</strong></p>
<p style="text-align: justify;"><strong>SUBTOPIK: KEDUDUKAN TITIK</strong></p>
<p style="text-align: justify;"><span style="background-color: transparent;">3. Perhatikan kubus ABCD.EFGH di bawah ini.</span></p>
<p style="text-align: justify;"><span style="background-color: transparent;"><img decoding="async" style="width: 268px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/11-129.png" alt="11-129" width="268" /></span></p>
<p style="text-align: justify;">Jika titik P, Q dan R berturut-turut terletak pada rusuk BF, AE dan BC maka pernyataan yang benar adalah ….</p>
<ol style="list-style-type: upper-alpha; text-align: justify;">
<li>Titik P berada pada bidang CDG</li>
<li>Titik Q berada pada bidang ABCD</li>
<li>Titik Q dan R sebidang</li>
<li>Titik R berada pada bidang ABD</li>
<li>Titik P, Q dan R sebidang</li>
</ol>
<p style="text-align: justify;"><strong>Jawaban D</strong></p>
<p style="text-align: justify;"><strong>Pembahasan :</strong></p>
<ul style="text-align: justify;">
<li>Titik P terletak pada bidang ABFE dan bidang BCGF</li>
<li>Titik Q terletak pada bidang ABFE dan bidang ADHE</li>
<li>Titik R terletak pada bidang ABCD dan bidang BCGF</li>
<li>Titik P dan Q sebidang (pada bidang ABFE)</li>
<li>Titik P dan R sebidang (pada bidang BCGF)</li>
</ul>
<p style="text-align: justify;">Jadi dari beberapa pernyataan di atas maka pernyataan yang benar pada pilihan jawaban adalah titik R berada pada bidang ABD, karena jika bidang ABD diperluas maka diperoleh bidang ABCD.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 820px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Untitled%20design%20(1)-24.png" alt="Untitled design (1)-24" width="820" /></p>
<p style="text-align: justify;"><strong>TOPIK: BIDANG RUANG (KEDUDUKAN DAN PROYEKSI)</strong></p>
<p style="text-align: justify;"><strong>SUBTOPIK: KEDUDUKAN GARIS TERHADAP BIDANG</strong></p>
<ol style="text-align: justify;" start="4">
<li>Perhatikan kubus ABCD.EFGH di bawah ini.</li>
</ol>
<p style="text-align: justify;"><img decoding="async" style="width: 208px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/12-19.png" alt="12-19" width="208" /></p>
<p style="text-align: justify;">Misalkan P adalah titik tengah ED. Bidang yang tegak lurus dengan garis AP adalah bidang ….</p>
<ol style="list-style-type: upper-alpha; text-align: justify;">
<li>BCHE</li>
<li>ADGF</li>
<li>CDEF</li>
<li>BDHF</li>
<li>ABGH</li>
</ol>
<p style="text-align: justify;"><strong>Jawaban C</strong></p>
<p style="text-align: justify;"><strong>Pembahasan :</strong></p>
<p style="text-align: justify;">Perhatikan bahwa karena P adalah titik tengah dari diagonal ED maka P juga menjadi titik tengah dari diagonal AH.</p>
<p style="text-align: justify;">Garis AP dapat diperpanjangan menjadi garis AH.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 224px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/13-17.png" alt="13-17" width="224" /></p>
<p style="text-align: justify;"><u>Garis AP dan bidang BCHE</u></p>
<p style="text-align: justify;">Perhatikan bahwa garis EF terletak pada bidang BCHE. Namun, garis AP tidak tegak lurus garis EH. Sehingga AP tidak tegak lurus bidang BCHE.</p>
<p style="text-align: justify;"><u>Garis AP dengan bidang ADGF</u></p>
<p style="text-align: justify;">Perhatikan bahwa garis AD terletak pada bidang ADGF. Namun, garis AP tidak tegak lurus dengan garis AD. Sehingga AP tidak tegak lurus bidang ADGF.</p>
<p style="text-align: justify;"><u>Garis AP dan bidang CDEF</u></p>
<p style="text-align: justify;">Perhatikan gambar di bawah ini.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 194px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/14-5577069081.png" alt="14-5577069081" width="194" /></p>
<p style="text-align: justify;">Perhatikan bahwa AH tegak lurus ED maka AP juga tegak lurus ED. Bidang yang memuat ED adalah bidang CDEF. Sehingga garis AP tegak lurus bidang CDEF.</p>
<p style="text-align: justify;"><u>Garis AP dan bidang BDHF</u></p>
<p style="text-align: justify;">Perhatikan bahwa garis DH berada pada bidang BDHF. Namun, garis AH (sebagai perpanjangan garis AP) tidak tegak lurus garis DH. Sehingga AP tidak tegak lurus bidang BDHF.</p>
<p style="text-align: justify;"><u>Garis AP dan bidang ABGH</u></p>
<p style="text-align: justify;">Garis AP tidak tegak lurus bidang ABGH karena gari AP terletak pada bidang ABGH.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 820px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Untitled%20design%20(1)-24.png" alt="Untitled design (1)-24" width="820" /></p>
<p style="text-align: justify;"><strong>TOPIK: BIDANG RUANG (KEDUDUKAN DAN PROYEKSI)</strong></p>
<p style="text-align: justify;"><strong>SUBTOPIK: PROYEKSI</strong></p>
<p style="text-align: justify;"><span style="background-color: transparent;">5. Perhatikan kubus ABCD.EFGH berikut ini.</span></p>
<p style="text-align: justify;"><img decoding="async" style="width: 233px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/15-14.png" alt="15-14" width="233" /></p>
<p style="text-align: justify;">Proyeksi bidang BFC ke bidang CHE adalah bidang….</p>
<ol style="list-style-type: upper-alpha; text-align: justify;">
<li>BCE</li>
<li>BCD</li>
<li>BCM dengan M titik tengan BE</li>
<li>BCN dengan N titik tengah CH</li>
<li>BCO dengan O titik tengah EH</li>
</ol>
<p style="text-align: justify;"><strong>Jawaban C</strong></p>
<p style="text-align: justify;"><strong>Pembahasan :</strong></p>
<p style="text-align: justify;">Perhatikan gambar di bawah ini.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 233px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/15-14.png" alt="15-14" width="233" /></p>
<p style="text-align: justify;">Bidang BFC jika diperluas maka akan menjadi bidang BCHE. Garis potong bidang BCHE dengan bidang BCE adalah garis BC. Kemudian proyeksikan titik F ke bidang BCHE.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 222px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/16-13.png" alt="16-13" width="222" /></p>
<p style="text-align: justify;">Misalkan titik M adalah titik potong diagonal sisi BE dan diagonal sisi AF. Maka titik M berada tepat pada pertengahan garis BE.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 209px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/17-11.png" alt="17-11" width="209" /></p>
<p style="text-align: justify;">Ingat kembali bahwa diagonal sisi pada kubus saling tegak lurus. Sehingga, proyeksi titik F ke bidang BCHE sama dengan proyeksi titik F ke garis BE, yaitu titik M.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 210px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/18-11.png" alt="18-11" width="210" /></p>
<p style="text-align: justify;">Jadi proyeksi bidang BCF ke bidang BCHE adalah bidang BCM dimana M adalah titik tengah BE.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 820px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Untitled%20design%20(1)-24.png" alt="Untitled design (1)-24" width="820" /></p>
<p style="text-align: justify;"><strong>TOPIK: BIDANG RUANG (JARAK)</strong></p>
<p style="text-align: justify;"><strong>SUBTOPIK: JARAK TITIK KE BIDANG</strong></p>
<p style="text-align: justify;">6. Diketahui sebuah kubus ABCD.EFGH dengan rusuk 6 cm. Jarak titik E ke bidang ACH adalah …. cm.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 223px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/19-10.png" alt="19-10" width="223" /></p>
<p style="text-align: justify;"><img decoding="async" style="width: 78px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/20-9.png" alt="20-9" width="78" /></p>
<p style="text-align: justify;"><strong>JAWABAN : B</strong></p>
<p style="text-align: justify;"><strong>PEMBAHASAN :</strong></p>
<p style="text-align: justify;">Jika kita tambahkan satu buah kubus lagi disebelah kiri kubus ABCD.EFGH kemudian perluas bidang ACH seperti pada gambar berikut ini.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 340px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/21-8.png" alt="21-8" width="340" /></p>
<p style="text-align: justify;">Sehingga jarak titik E ke bidang ACH sama dengan jarak titik E ke garis AP’, atau sama juga dengan jarak titik D ke titik O.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 217px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/22-9.png" alt="22-9" width="217" /></p>
<p style="text-align: justify;">Sehingga dengan persamaan luas segitiga DHP diperoleh :</p>
<p style="text-align: justify;"><img decoding="async" style="width: 196px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/23-6.png" alt="23-6" width="196" /></p>
<p style="text-align: justify;">Jadi Jarak titik E ke bidang ACH adalah <img decoding="async" style="width: 55px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/24-5.png" alt="24-5" width="55" /></p>
<p style="text-align: justify;"><img decoding="async" style="width: 820px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Untitled%20design%20(1)-24.png" alt="Untitled design (1)-24" width="820" /></p>
<p style="text-align: justify;"><strong>TOPIK: BIDANG RUANG (JARAK)</strong></p>
<p style="text-align: justify;"><strong>SUBTOPIK: JARAK DUA BIDANG SEJAJAR</strong></p>
<p style="text-align: justify;"><span style="background-color: transparent;">7. Diketahui kubus ABCD.EFGH dengan panjang rusuk 10 cm. Jarak bidang ACH dengan bidang BEG adalah …. cm</span></p>
<p style="text-align: justify;"><img decoding="async" style="width: 234px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/25-5.png" alt="25-5" width="234" /></p>
<p style="text-align: justify;"><img decoding="async" style="width: 67px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/26-4.png" alt="26-4" width="67" /></p>
<p style="text-align: justify;"><strong>JAWABAN : A</strong></p>
<p style="text-align: justify;"><strong>PEMBAHASAN :</strong></p>
<p style="text-align: justify;">Untuk memudahkan buat bidang diagonal BDHF dengan titik M dan titik N adalah titik tengah perpotongan diagonal atap dan alas seperti gambar berikut.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 226px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/27-4.png" alt="27-4" width="226" /></p>
<p style="text-align: justify;">Bidang BEG berptongan dengan bidang BDHF di garis BM. Sedangkan bidang ACH berpotongan dengan bidang BDHF di garis HN.</p>
<p style="text-align: justify;">Jika kita buat segitiga BMN pada bidang diagonal BDHF maka jarak bidang ACH ke bidang BEG sama dengan jarak titik N ke garis BM atau sama dengan NO.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 200px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/28-4.png" alt="28-4" width="200" /></p>
<p style="text-align: justify;">Dengan persamaan luas segitiga BMN maka diperoleh :</p>
<p style="text-align: justify;"><img decoding="async" style="width: 180px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/29-3.png" alt="29-3" width="180" /></p>
<p style="text-align: justify;">Jadi jarak bidang ACH ke bidang BEG adalah <img decoding="async" style="width: 69px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/30-2.png" alt="30-2" width="69" /></p>
<p style="text-align: justify;"><img decoding="async" style="width: 820px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Untitled%20design%20(1)-24.png" alt="Untitled design (1)-24" width="820" /></p>
<p style="text-align: justify;"><strong>TOPIK: BIDANG RUANG (SUDUT)</strong></p>
<p style="text-align: justify;"><strong>SUBTOPIK: SUDUT DUA GARIS</strong></p>
<p style="text-align: justify;"><span style="background-color: transparent;">8. Diketahui kubus ABCH.EFGH dengan rusuk 4 cm. Titik T membagi dua rusuk BC menjadi dua bagian. Jika <img decoding="async" style="width: 17px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/31-2.png" alt="31-2" width="17" />adalah sudut antara garis HT dengan garis BG maka <img decoding="async" style="width: 82px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/32-1.png" alt="32-1" width="82" /></span></p>
<p><img decoding="async" style="width: 64px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/33-4.png" alt="33-4" width="64" /></p>
<p style="text-align: justify;"><strong>Jawaban </strong><strong>C</strong></p>
<p style="text-align: justify;"><strong>Pembahasan :</strong></p>
<p style="text-align: justify;">Perhatikan kubus di bawah :</p>
<p style="text-align: justify;"><img decoding="async" style="width: 317px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/34-1.png" alt="34-1" width="317" /></p>
<p style="text-align: justify;">Kemudian pada segitiga ATH, misalkan R adalah titik pada AH sehingga garis TR tegak lurus garis AH.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 174px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/35-1.png" alt="35-1" width="174" /></p>
<p style="text-align: justify;">Dengan aturan cos maka diperoleh,</p>
<p style="text-align: justify;"><img decoding="async" style="width: 247px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/36-1.png" alt="36-1" width="247" /></p>
<p style="text-align: justify;">Kemudian hitung nilai sin <img decoding="async" style="width: 17px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/31-2.png" alt="31-2" width="17" /> dengan rumus identitas trigonometri berikut :</p>
<p style="text-align: justify;"><img decoding="async" style="width: 390px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/37-1.png" alt="37-1" width="390" /></p>
<p style="text-align: justify;">Jadi nilai dari <img decoding="async" style="width: 157px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/38-1.png" alt="38-1" width="157" /></p>
<p style="text-align: justify;"><img decoding="async" style="width: 820px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Untitled%20design%20(1)-24.png" alt="Untitled design (1)-24" width="820" /></p>
<p style="text-align: justify;"><strong>TOPIK: BIDANG RUANG (SUDUT)</strong></p>
<p style="text-align: justify;"><strong>SUBTOPIK: SUDUT GARIS DAN BIDANG</strong></p>
<p style="text-align: justify;"><span style="background-color: transparent;">9. Diketahui sebuah kubus ABCD.EFGH dengan panjang sisi kubus <img decoding="async" style="width: 33px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/39-1.png" alt="39-1" width="33" />. Sinus sudut antara rusuk BF ke bidang BEG adalah….</span></p>
<p style="text-align: justify;"><strong><img decoding="async" style="width: 68px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/40-1.png" alt="40-1" width="68" /></strong></p>
<p style="text-align: justify;"><strong>Jawaban B</strong></p>
<p style="text-align: justify;"><strong>Pembahasan :</strong></p>
<p style="text-align: justify;">Perhatikan gambar di bawah ini.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 209px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/41-1.png" alt="41-1" width="209" /></p>
<p style="text-align: justify;">Diketahui :</p>
<p style="text-align: justify;"><img decoding="async" style="width: 77px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/42-1.png" alt="42-1" width="77" /></p>
<p style="text-align: justify;">Sehingga,</p>
<p style="text-align: justify;"><img decoding="async" style="width: 426px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/43-1.png" alt="43-1" width="426" /></p>
<p style="text-align: justify;">Maka,</p>
<p style="text-align: justify;"><img decoding="async" style="width: 269px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/44-1.png" alt="44-1" width="269" /></p>
<p style="text-align: justify;">Sinus sudut antara rusuk BF ke bidang BEG adalah <img decoding="async" style="width: 35px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/45-1.png" alt="45-1" width="35" /></p>
<p style="text-align: justify;"><img decoding="async" style="width: 820px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Untitled%20design%20(1)-24.png" alt="Untitled design (1)-24" width="820" /></p>
<p style="text-align: justify;"><strong>TOPIK: BIDANG RUANG (SUDUT)</strong></p>
<p style="text-align: justify;"><strong>SUBTOPIK: IRISAN BIDANG</strong></p>
<p style="text-align: justify;"><span style="background-color: transparent;">10. Diketahui kubus ABCD.EFGH dengan titik M adalah titik tengah rusuk CG. Irisan bidang yang melalu titik M, D dan F adalah ….</span></p>
<ol style="list-style-type: upper-alpha; text-align: justify;">
<li><span style="background-color: transparent;">Segitiga</span></li>
<li><span style="background-color: transparent;">Segitiga sama sisi</span></li>
<li><span style="background-color: transparent;">Segiempat</span></li>
<li><span style="background-color: transparent;">Segilima</span></li>
<li><span style="background-color: transparent;">Persegi</span></li>
</ol>
<p style="text-align: justify;"><strong>Jawaban C</strong></p>
<p style="text-align: justify;"><strong>Pembahasan :</strong></p>
<p style="text-align: justify;">Perhatikan gambar di bawah ini.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 236px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/46-1.png" alt="46-1" width="236" /></p>
<p style="text-align: justify;">Karena titik D terletak pada rusuk yang bersebrangan dengan titik F maka titik M akan berseberangan pula dengan titik lain di rusuk AE. Misalkan titik N adalah titik tengah rusuk AE.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 241px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/47-1.png" alt="47-1" width="241" /></p>
<p style="text-align: justify;">Sehingga bidang yang terbentuk adalah bidang segiempat NDFM seperti pada gambar di atas.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 820px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Untitled%20design%20(1)-24.png" alt="Untitled design (1)-24" width="820" /></p>
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plugins: [analyticsTrackable()],
});
/* Additional context tracker pageView */
const post_id = 7804;
const tags_id = [76,10,172,37];
const category_id = 552;
const sub_category_id = 561;
const customData = {
tags_id: tags_id,
category_id: category_id,
sub_category_id: sub_category_id,
post_id: post_id,
};
Analytics.plugins.trackable.context(JSON.stringify(customData));
Analytics.ready(function () {
Analytics.page();
});
$(document).on('click', '[data-tracking-event-type]', function (event) {
const eventType = $(this).data('tracking-event-type');
const context = $(this).data('tracking-context');
Analytics.track(eventType, context);
});
</script>
<footer class="footer">
<div class="container">
<div class="row">
<div class="col-lg-3">
<div class="office">
<a href="https://www.ruangguru.com/">
<img src="https://cdn-web-2.ruangguru.com/static/RG_LOGO_WHITE.png?convert=auto" alt="Logo Ruangguru" loading="lazy" />
</a>
<address>
<p class="hq">RUANGGURU HQ</p>
<p>
Gedung Sinarmas MSIG Tower Lt. 33. Jl. Jenderal Sudirman Kav. 21, Karet Kuningan, Setiabudi, Jakarta Selatan, Jakarta 12920
</p>
</address>
</div>
<nav class="footer-menu call-us">
<p class="title">Hubungi Kami</p>
<address>
<a href="mailto:info@ruangguru.com">
<img class="icon-call-us" src="https://cdn-web-2.ruangguru.com/file-uploader/lp/4739a139-8f09-42ea-b517-d842c5d1c28d.png" loading="lazy" alt="Logo Email Footer" />
info@ruangguru.com</a>
<a href="tel:02130930000">
<img class="icon-call-us" src="https://cdn-web-2.ruangguru.com/file-uploader/lp/6f4bb6c8-52c9-4acb-859b-47a10a7eec75.png" loading="lazy" alt="Logo Phone Footer" />(021) 3093 0000</a>
<a href="https://wa.me/6281574410000">
<img class="icon-call-us" src="https://cdn-web-2.ruangguru.com/file-uploader/lp/4b58468a-b2f9-40e4-867f-d3242a065dcf.png" loading="lazy" alt="Logo Whatsapp Footer" />0815 7441 0000</a>
</address>
</nav>
<nav class="footer-menu social d-none d-lg-block">
<p class="title">Ikuti Kami</p>
<a target="_blank" href="https://www.instagram.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/instagram.png" loading="lazy" alt="Logo Instagram Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.facebook.com/ruanggurucom/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/facebook.png" loading="lazy" alt="Logo Facebook Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://twitter.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/twitter.png" loading=" lazy" alt="Logo Twitter Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.youtube.com/ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/youtube.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/youtube.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/youtube.png" loading=" lazy" alt="Logo Youtube Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.linkedin.com/company/ruangguru-com">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/linkedin.png" loading=" lazy" alt="Logo LinkedIn Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.tiktok.com/@ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/tiktok.png" loading=" lazy" alt="Logo TikTok Footer" width="32px" height="32px" />
</picture>
</a>
</nav>
</div>
<div class="col-lg-9">
<div class="row">
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title">Produk Ruangguru</p>
<ul type="none">
<li><a href="https://roboguru.ruangguru.com" target="_blank">Roboguru</a></li>
<li><a href="https://www.ruangguru.com/roboguruplus">Roboguru Plus</a></li>
<li><a href="https://www.ruangguru.com/dafa-lulu">Dafa dan Lulu</a></li>
<li><a href="https://www.ruangguru.com/for-kids/kursus">Kursus for Kids</a></li>
<li><a href="https://www.ruangguru.com/for-kids">Ruangguru for Kids</a></li>
<li><a href="https://www.ruangguru.com/bisnis">Ruangguru for Business</a></li>
<li><a href="https://www.ruangguru.com/ruanguji">Ruanguji</a></li>
<li><a href="https://www.ruangguru.com/blog">Ruangbaca</a></li>
<li><a href="https://www.ruangguru.com/ruangkelas">Ruangkelas</a></li>
<li><a href="https://www.ruangguru.com/ruangbelajar">Ruangbelajar</a></li>
<li><a href="https://pengajar.ruangguru.com/">Ruangpengajar</a></li>
<li><a href="https://www.ruangguru.com/privat">Ruangguru Privat</a></li>
<li><a href="https://www.ruangpeduli.org/" target="_blank">Ruangpeduli</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title">Bantuan & Panduan</p>
<ul type="none">
<li><a href="https://www.ruangguru.com/company-credentials">Company Credentials</a></li>
<li><a href="https://www.ruangguru.com/beasiswa">Beasiswa Ruangguru</a></li>
<li><a href="https://www.ruangguru.com/cicilan">Cicilan Ruangguru</a></li>
<li><a href="https://www.ruangguru.com/promo">Promo Ruangguru</a></li>
<li><a href="https://ticketing.ruangguru.com/help?request_type_id=459" target="_blank">Vulnerability Report</a></li>
<li><a href="https://www.ruangguru.com/bantuan#layanan">Layanan Pengaduan</a></li>
<li><a href="https://www.ruangguru.com/terms-conditions">Syarat & Ketentuan</a></li>
<li><a href="https://www.ruangguru.com/privacy-policy">Kebijakan Privasi</a></li>
<li><a href="https://www.ruangguru.com/about-us">Tentang Kami</a></li>
<li><a href="https://www.ruangguru.com/contact-us">Kontak Kami</a></li>
<li><a href="https://www.ruangguru.com/press">Press Kit</a></li>
<li><a href="https://www.ruangguru.com/bantuan">Bantuan</a></li>
<li><a href="https://career.ruangguru.com/">Karier</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title">Produk Lainnya</p>
<ul type="none">
<li><a href="https://www.brainacademy.id/" target="_blank">Brain Academy</a></li>
<li><a href="https://www.english-academy.id/" target="_blank">English Academy</a></li>
<li><a href="https://skillacademy.com/" target="_blank">Skill Academy</a></li>
<li><a href="https://www.ruangkerja.id/" target="_blank">Ruangkerja</a></li>
<li><a href="https://www.schoters.com/id/" target="_blank">Schoters</a></li>
<li><a href="https://www.kalananti.id/" target="_blank">Kalananti</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title"> Coba GRATIS Aplikasi Ruangguru</p>
<div class="download-list">
<ul>
<li>
<a target="_blank" rel="nofollow" href="https://apps.apple.com/id/app/ruangguru-solusi-belajar/id1099742206?l=id">
<img src="https://cdn-web-2.ruangguru.com/static/appstore.png" loading="lazy" alt="Button App Store Footer " />
</a>
</li>
<li>
<a target="_blank" rel="nofollow" href="https://play.google.com/store/apps/details?id=com.ruangguru.livestudents&hl=in">
<img src="https://cdn-web-2.ruangguru.com/static/googleplay.png" loading="lazy" alt="Button Google Play Footer " />
</a>
</li>
<li>
<a target="_blank" rel="nofollow" href="https://appgallery.huawei.com/#/app/C102352375">
<img src="https://cdn-web-2.ruangguru.com/static/huawei.png" loading="lazy" alt="Button AppGallery Footer " />
</a>
</li>
</ul>
</div>
</nav>
</div>
</div>
</div>
</div>
<div class="d-lg-none text-center">
<nav class="footer-menu social">
<p class="title">Ikuti Kami</p>
<a target="_blank" href="https://www.instagram.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/instagram.png" loading="lazy" alt="Logo Instagram Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.facebook.com/ruanggurucom/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/facebook.png" loading="lazy" alt="Logo Facebook Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://twitter.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/twitter.png" loading=" lazy" alt="Logo Twitter Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.youtube.com/ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/youtube.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/youtube.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/youtube.png" loading=" lazy" alt="Logo Youtube Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.linkedin.com/company/ruangguru-com">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/linkedin.png" loading=" lazy" alt="Logo LinkedIn Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.tiktok.com/@ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/tiktok.png" loading=" lazy" alt="Logo TikTok Footer" width="32px" height="32px" />
</picture>
</a>
</nav>
</div>
<p class="footer-copyright">
© 2026 All Rights Reserved PT. Ruang Raya Indonesia
</p>
</div>
<style>
.bantuan-container {
position: relative;
}
.bantuan-element {
position: fixed;
z-index: 999;
display: flex;
align-items: flex-end;
justify-content: flex-end;
cursor: pointer;
transition: all 0.6s ease;
}
.bantuan-top {
bottom: 11rem;
right: 2rem;
}
.bantuan-bottom {
bottom: 2rem;
right: 2rem;
}
.bantuan-top-2 {
bottom: 15rem;
right: 2rem;
}
.bantuan-top-3 {
bottom: 19rem;
right: 2rem;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 2rem;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 2rem;
}
@media (min-width: 768px) {
.bantuan-element img {
width: auto;
transition: all 0.4s ease;
}
.bantuan-top img {
width: 140px;
}
.bantuan-bottom img {
width: 140px;
}
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 140px;
}
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 140px;
}
.bantuan-element.clicked {
bottom: 9rem;
right: 2.5rem;
}
.bantuan-element.clicked img {
width: auto;
height: 64px;
}
}
@media (max-width: 767px) {
.bantuan-top {
bottom: 8rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom {
bottom: 2rem;
right: 1.25rem;
align-items: center;
}
.bantuan-top-2 {
bottom: 12rem;
right: 1rem;
align-items: center;
}
.bantuan-top-3 {
bottom: 16rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 1.25rem;
align-items: center;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 1.25rem;
align-items: center;
}
.bantuan-element img {
width: auto;
}
.bantuan-top img,
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 96px;
}
.bantuan-bottom img,
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 96px;
}
}
.bantuan-element:hover {
transform: scale(1.05);
}
.bantuan-element img {
max-width: 100%;
height: auto;
}
</style>
<div id="bantuan-divs-container" style="position: relative" data-product="ruangguru" data-table="rg_floating_icon"></div>
<script>
class FloatingDivsComponent {
constructor(product = 'ruangguru', table = 'rg_floating_icon') {
this.container = document.getElementById('bantuan-divs-container');
this.floatingElements = [];
this.product = product;
this.table = table;
// Configuration
this.config = {
baseApiUrl: 'https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/rg_banner/views/',
apiKey: 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
maxElements: 2,
zIndexBase: 100,
};
// Build dynamic API URL based on table parameter
this.config.apiUrl = this.buildApiUrl();
this.init();
}
buildApiUrl() {
const baseUrl = this.config.baseApiUrl;
const tableName = this.table || 'rg_floating_icon';
const queryParams =
'offset=0&limit=99999&sort=rankPosition&where=(type,eq,floating)~and(showIn,anyof,blog)~and(hide,is,false)~and(product,eq,' +
this.product +
')&nested%5Bcta%5D%5Bfields%5D=Id,name,ctaId,imageUrl,ctaLink,targetUrl';
return `${baseUrl}${tableName}?${queryParams}`;
}
async init() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to initialize floating divs component:', error);
}
}
async fetchFloatingElements() {
try {
const options = {
method: 'GET',
headers: {
'xc-token': this.config.apiKey || 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
},
};
const urlNoco = this.config.apiUrl;
const response = await fetch(urlNoco, options);
if (!response.ok) {
throw new Error(`HTTP error! status: ${response.status}`);
}
const data = await response.json();
this.floatingElements = this.processApiResponse(data);
} catch (error) {
console.error('Error fetching floating elements:', error);
throw error;
}
}
processApiResponse(data) {
if (!data || !data.list || !Array.isArray(data.list)) {
return [];
}
console.log(data.list);
// Ensure we only get maximum 2 elements
const limitedElements = data.list.slice(0, this.config.maxElements);
return limitedElements;
}
renderFloatingElements() {
if (!this.container || this.floatingElements.length === 0) {
return;
}
// Additional safeguard: ensure we never render more than maxElements
const elementsToRender = this.floatingElements.slice(0, this.config.maxElements);
// Clean up existing elements and their event listeners
this.cleanupExistingElements();
// Clear existing content
this.container.innerHTML = '';
elementsToRender.forEach((element, index) => {
const floatingDiv = this.createFloatingDiv(element, index);
this.container.appendChild(floatingDiv);
});
}
cleanupExistingElements() {
// Clear existing elements (no need for event listener cleanup with CSS approach)
const existingElements = this.container.querySelectorAll('[data-floating-element]');
existingElements.forEach(element => {
element.remove();
});
}
createFloatingDiv(element, index) {
const div = document.createElement('div');
const cta = element.cta[0]; // Use the first CTA
// Add data attribute for cleanup tracking
div.setAttribute('data-floating-element', 'true');
// Apply CSS classes based on rankPosition
const positionClass = this.getPositionClass(element.rankPosition, index);
div.className = `bantuan-element ${positionClass}`;
div.style.zIndex = this.config.zIndexBase + index;
// Create the link and image
const link = document.createElement('a');
link.href = 'https://cta.ruangguru.com/' + cta.ctaId || '#';
link.target = '_blank';
// Add tracking attributes
link.setAttribute('data-tracking-event-type', 'landing_page__core__item_click');
link.setAttribute(
'data-tracking-context',
JSON.stringify({
product_name: this.product,
cta_action: 'redirection',
cta_action_detail: link.href,
item_type: 'floating',
item_name: element.name || 'Floating element',
item_category: 'payment',
item_position: index,
item_serial: null,
section_type: 'floating_item',
section_position: 'body',
section_name: 'floating_item',
})
);
const img = document.createElement('img');
img.src = element.imageUrl + '?h=200&convert=webp';
img.alt = element.name || 'Floating element';
img.loading = 'lazy';
// Add click tracking
link.addEventListener('click', () => {
this.trackClick(element, cta);
});
link.appendChild(img);
div.appendChild(link);
return div;
}
getPositionClass(rankPosition, index) {
// Define positioning classes based on rankPosition
if (rankPosition === 1) {
return 'bantuan-top'; // Top position
} else if (rankPosition === 2) {
return 'bantuan-bottom'; // Bottom position
} else {
// For additional elements, distribute them evenly
return `bantuan-${index % 2 === 0 ? 'top' : 'bottom'}-${Math.floor(index / 2) + 1}`;
}
}
trackClick(element, cta) {
// Implement click tracking logic here
console.log('Floating element clicked:', {
elementId: element.Id,
elementName: cta.name,
ctaId: cta.ctaId,
targetUrl: cta.targetUrl,
});
}
// Public method to manually refresh
async refresh() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to refresh floating elements:', error);
throw error;
}
}
// Public method to get current floating elements
getFloatingElements() {
return [...this.floatingElements];
}
}
// Initialize the component when DOM is ready
document.addEventListener('DOMContentLoaded', () => {
// Get product and table parameters from data attributes
const container = document.getElementById('bantuan-divs-container');
const product = container.getAttribute('data-product') || 'ruangguru';
const table = container.getAttribute('data-table') || 'rg_floating_icon';
new FloatingDivsComponent(product, table);
});
// Export for use in other modules if needed
if (typeof module !== 'undefined' && module.exports) {
module.exports = FloatingDivsComponent;
}
</script> <div id="wp-install-nudge" style="
position: fixed;
bottom: 0rem;
right: 0;
z-index: 999;
cursor: pointer;
"></div>
<script>
(function (w, d, s, o, f, js, fjs) {
w['Sales-Nudge-Widget'] = o; w[o] = w[o] || function () { (w[o].q = w[o].q || []).push(arguments) };
js = d.createElement(s), fjs = d.getElementsByTagName(s)[0];
js.id = o; js.src = f; js.async = 1; fjs.parentNode.insertBefore(js, fjs);
}(window, document, 'script', 'wpInstallNudge', 'https://cdn-web-2.ruangguru.com/sales-nudge/6198a95130/dist/widget.js'));
wpInstallNudge('init', { targetElementId: 'wp-install-nudge', clientTarget: 'ruangguru_blog' });
</script>
<script>
// note: disabled due to auto reload page
// var lastScrollTop = 0;
// $(window).scroll(function(event){
// var st = $(this).scrollTop();
// if (st > lastScrollTop){
// $('#wp-install-nudge').slideDown( "slow", function() {});
// } else {
// $('#wp-install-nudge').slideUp( "slow", function() {});
// }
// lastScrollTop = st;
// });
// $(document).ready(function () {
// $("#wp-install-nudge").hide();
// });
$('#wp-install-nudge').click(function(){
Analytics.track("promotion__install_nudge__click",
{
user_email: "ruangguru@blog.com",
cta_link: widgetData.dataConfig.target_link
}).catch((err) => {
console.log("tracker error", err);
});
});
</script>
</footer>
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async function getCtaDetails(ctaIds) {
const endpoint =
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const ctaList = data?.list || [];
const ctaMap = new Map();
for (const ctaData of ctaList) {
ctaMap.set(ctaData.ctaId, ctaData);
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return ctaMap;
} catch (error) {
console.error("Error fetching CTA details:", error);
return new Map();
}
}
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const regex = /{{cta\((‘(.*?)’|“(.*?)”)\)}}/g;
const bodyHTML = document.body.innerHTML;
const matches = Array.from(bodyHTML.matchAll(regex));
const ctaIds = matches.map((match) => {
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return ctaId;
});
const ctaMap = await getCtaDetails(ctaIds);
const replacedHTML = bodyHTML.replace(regex, (match, _inner, ctaId1, ctaId2) => {
const ctaId = ctaId1 ?? ctaId2;
const ctaData = ctaMap.get(ctaId);
if (ctaData) {
return `<a href="https://cta.ruangguru.com/${ctaData.ctaId}" target="_${ctaData.targetType}" style="position:relative;display:inline-block;">
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} else {
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}
});
document.body.innerHTML = replacedHTML;
}
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