Ada apa aja sih unsur-unsur lingkaran itu? Bagaimana cara menghitungnya? Yuk simak cara menghitung unsur-unsur lingkaran dalam artikel Matematika kelas 8 ini!
—
Hai haiii! Kalian masih ingat kan apa saja unsur-unsur lingkaran? Unsur lingkaran itu bukan meliputi angin, air, api, dan udara yang dikuasai Avatar the Legend of Aang, ya, hehehe.
Coba sebutkan apa saja unsur lingkaran!
(kalo kamu masih inget, cus ke kolom komentar bawah dong :P)
Unsur lingkaran itu terdiri dari titik pusat, jari-jari (r), diameter (d), tali busur, busur, juring, tembereng, dan apotema. Masih inget kan?
Kalau kamu masih lupa-lupa ingat, coba perhatikan gambar di bawah ini ya!
(sumber: Video Belajar Ruangguru)
- Titik Pusat (titik O)
- Jari-jari (ruas garis OA, OB, OC, OD).
- Diameter (ruas garis AB)
- Tali Busur (ruas garis AD dan AB)
- Busur (garis lengkung AD, DC, AB)
- Juring (daerah BOC)
- Tembereng (daerah warna biru)
- Apotema (ruas garis OE)
Nah, kalau kamu udah inget tentang masing-masing perbedaan unsur-unsur lingkaran tersebut, sekarang kita akan lanjut mencari tahu tentang cara menghitung unsur-unsur lingkaran. Simak baik-baik ya!
Baca Juga: Rumus Luas dan Volume Kubus serta Contoh Soal
1. Rumus Keliling dan Luas Lingkaran
Apa bedanya keliling lingkaran dan luas lingkaran? Keliling lingkaran adalah panjang garis lengkung dari suatu lingkaran, sedangkan luas lingkaran merupakan luas daerah yang dibatasi oleh busur lingkaran atau keliling lingkaran.
Berikut rumus untuk menghitung keliling dan luas lingkaran.
Contoh Soal!
1. Diketahui lingkaran dengan jari-jari 20 cm, keliling lingkaran tersebut adalah …
Pembahasan:
Diketahui: r = 20 cm
Ditanya: Keliling lingkaran (K) …?
Jawab:
K = 2 × π × r
K = 2 × 3,14 × 20
K = 125,6 cm
Jadi, keliling lingkaran tersebut adalah 125,6 cm.
2. Jika diketahui sebuah lingkaran mempunyai diameter 10 cm. Berapakah luas lingkaran tersebut?
Pembahasan:
Diketahui: d = 10 cm
Ditanya: Luas lingkaran (L) …?
Jawab:
L = 1/4 × π × d2
L = (1/4) × 3,14 × (10)2
L = (1/4) × 314
L = 78,5 cm2
Jadi, luas lingkaran tersebut adalah 78,5 cm2.
2. Rumus Menghitung Sudut Pusat dan Sudut Keliling
Ngejar Si Mamat makin bikin pusing (Tjakeeeep~~~)
Yuk, belajar sudut pusat dan sudut keliling.
Sama-sama sudut yang ada di lingkaran tapi mereka berdua beda. Kadang kalau ga paham konsep, bisa bingung bedain keduanya. Tapi santuy, bareng Ruangguru, kamu jadi bisa ngebedain antara sudut pusat dan sudut keliling. Perhatiin deh pengertiannya sama gambarnya.
(sumber: Video Belajar Ruangguru)
Sudut pusat itu merupakan daerah sudut yang dibatasi oleh dua jari-jari lingkaran yang titik sudutnya merupakan titik pusat lingkaran. Contoh: ∠AOB.
Nah, kalau sudut keliling merupakan daerah sudut yang dibatasi oleh dua tali busur yang berpotongan di satu titik pada lingkaran dan titik sudutnya terletak pada keliling lingkaran. Contoh: ∠ADB dan ∠ACB.
Udah tau bedanya?
Oke walaupun mereka beda, tapi mereka tuh nggak putus hubungan ya.
Ada hubungan antara sudut pusat dan sudut keliling lingkaran.
Kalau keduanya menghadap busur yang sama maka besar sudut pusat bakal sama dengan dua kalinya besar sudut keliling.
Baca Juga: Kedudukan Titik dan Garis Lurus terhadap Lingkaran
Oh ya, biar kamu makin kenal sama sudut keliling, ga ada salahnya kamu pelajari sifat dari sudut keliling yaa biar jadi bestiie!
a. Besar sudut keliling yang menghadap diameter lingkaran adalah 90°
(sumber: Video Belajar Ruangguru)
b. Besar sudut-sudut keliling yang menghadap busur yang sama adalah sama besar
(sumber: Video Belajar Ruangguru)
c. Jumlah besar sudut-sudut yang berhadapan pada segi empat tali busur (Segi empat yang sisinya tali busur) adalah 180°
(sumber: Video Belajar Ruangguru)
Contoh Soal!
Sebuah lingkaran memiliki besar ∠ABC = 60° dan ∠AOC = (4x – 12)°. Berapakah nilai x pada lingkaran tersebut?
Pembahasan:
Diketahui:
Sudut keliling lingkaran = ∠ABC = 60°
Sudut pusat lingkaran = ∠AOC = (4x – 12)°
Ditanya: Nilai x …?
Jawab:
∠AOC = 2 × ∠ABC
(4x – 12)° = 2 × 60°
(4x – 12)° = 120°
4x = 120° + 12°
4x = 132°
x = 33°
Jadi, didapat nilai x-nya adalah 33º. Sehingga, kita bisa tahu juga nih nilai sudut pusat lingkaran tersebut, yaitu:
∠AOC = (4x – 12)°
∠AOC = (4(33) – 12)°
∠AOC = (132 – 12)° = 120°
Berdasarkan perhitungan di atas, didapat nilai ∠AOC = 120°
3. Rumus Panjang Busur dan Luas Juring
Busur dalam lingkaran itu bukan seperti busur yang digunakan untuk memanah ya guys.
Busur bukan juga istri dari Pak Sur, hehehe.
Dalam matematika, busur adalah garis lengkung yang terletak pada lengkungan lingkaran dan menghubungkan dua titik pada keliling lingkaran. Contohnya garis lengkung AB.
(sumber: Video Belajar Ruangguru)
Nah kalau juring itu daerah di dalem lingkaran yang dibatasi oleh dua jari-jari dan satu busur lingkaran. Contohnya luas juring AOB.
Perlu kamu ketahui nih, buat cari panjang suatu busur dan luas juring, ada kaitannya sama sudut pusat lingkaran yang udah kamu pelajari di awal. Jangan kamu lupain ya.
Untuk mencari panjang busur lingkaran, kamu bisa dapetin dengan konsep perbandingan antara besar sudut pusat yang menghadap busur dan panjang busur dibanding dengan besar sudut lingkaran dan panjang keliling lingkaran. Konsepnya kalau disederhanakan langsung kaya gini nih.
Sementara untuk mendapatkan luas juring, kamu bisa menggunakan konsep perbandingan antara besar sudut pusat yang menghadap busur dan luas juring yang dibatasi busur, dibanding dengan besar sudut lingkaran dan luas lingkaran. Rumusnya jadi seperti ini:
Dari dua konsep panjang busur dan luas juring di atas, kamu bisa membuat hubungan spesial dari keduanya yang bisa bantu kamu menyelesaikan suatu masalah.
Kalau misal diketahui busur dan juringnya punya sudut pusat yang sama, terus ditanyakan salah satunya, kamu tinggal selesaikan menggunakan konsep perbandingan kaya gini.
Baca Juga: Cara Mencari Kemiringan (Gradien) pada Garis Lurus
Tapi kalau misalnya busur atau juringnya punya sudut yang berbeda, kamu juga bisa tetap menggunakan konsep perbandingan dengan membandingkan sudut pusat yang diketahui.
(sumber: Video Belajar Ruangguru)
4. Rumus Luas Tembereng
Apa itu tembereng?
Tembereng adalah daerah yang dibatasi oleh tali busur dan busur lingkaran. Dari gambar di atas, temberengnya adalah daerah yang berwarna biru.
Kalau mau cari luas tembereng, sebenarnya itu guampang pol, kalau udah diketahui luas juring dan luas segitiga. Karena kalau kamu liat lagi gambarnya tuh, luas daerah tembereng AD itu sama kaya luas juring di atasnya, yaitu luas juring AOD yang dikurangi luas segitiga AOD.
Nah, itu tadi penjelasan lengkap mengenai cara menghitung unsur-unsur lingkaran. Semoga kamu semakin paham yah! Kalau kamu pengen tambah ngerti penjelasan dalam artikel ini, gabung yuk di ruangbelajar.
Ada banyak video belajar pake animasi, rangkuman kece, latian soal yang mudah sampe menantang, dan bahkan ada game nya juga yang bisa bikin kamu cinta buat belajar.
Referensi:
Raharjo M, Setiawan A. (2018) Matematika SMP/MTs Kelas VIII. Jakarta: Erlangga
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<h1 class="content-title">
Rumus Menghitung Unsur-Unsur Lingkaran & Contoh | Matematika Kelas 8 </h1>
<div class="content-meta">
<p class="content-author"><a href="https://www.ruangguru.com/blog/author/adya-rosyada-yonas" class="">Adya Rosyada Yonas</a> </p>
<p class="content-info"><span>February 23, 2023 • </span> <span>6 minutes read</span></p>
<br />
</div>
<div class="content-body">
<p><span style="color: #000000;"><img decoding="async" style="width: 751px; display: block; margin: 0px auto; height: auto; max-width: 100%;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/MATEMATIKA%20%20VIII%20(1).png" alt="cara menghitung unsur lingkaran" /></span></p>
<blockquote>
<p style="text-align: center;"><em>Ada apa aja sih unsur-unsur lingkaran itu? Bagaimana cara menghitungnya? Yuk simak cara menghitung unsur-unsur lingkaran dalam artikel <strong><a href="https://www.ruangguru.com/blog/c/matematika/matematika-smp-kelas-8" target="_blank" rel="noopener">Matematika kelas 8</a></strong> ini!</em></p>
<p style="text-align: center;"><em>—</em></p>
</blockquote>
<p> </p>
<p style="text-align: justify;">Hai haiii! Kalian masih ingat kan apa saja <strong><a href="/blog/pengertian-dan-unsur-unsur-lingkaran" target="_blank" rel="noopener">unsur-unsur lingkaran</a></strong>? Unsur lingkaran itu bukan meliputi angin, air, api, dan udara yang dikuasai <em>Avatar the Legend of Aang</em>, ya, hehehe.</p>
<p style="text-align: justify;">Coba sebutkan apa saja unsur lingkaran!</p>
<p style="text-align: justify;">(kalo kamu masih inget, cus ke kolom komentar bawah dong :P)</p>
<p style="text-align: justify;">Unsur lingkaran itu terdiri dari <strong>titik pusat, jari-jari (r), diameter (d), tali busur, busur, juring, tembereng, dan apotema</strong>. Masih inget kan?</p>
<p style="text-align: justify;">Kalau kamu masih lupa-lupa ingat, coba perhatikan gambar di bawah ini ya!</p>
<p> </p>
<h2><span style="font-size: 18pt;">Unsur-Unsur Lingkaran</span></h2>
<p style="text-align: justify;"><img fetchpriority="high" decoding="async" style="width: 339px; height: auto; max-width: 100%; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Feb-23-2023-05-25-32-9044-AM.png" alt="unsur-unsur lingkaran" width="339" height="290" /></p>
<p style="text-align: center;"><em>(sumber: Video Belajar Ruangguru)</em></p>
<p> </p>
<ul>
<li style="text-align: justify;">Titik Pusat (titik O)</li>
<li style="text-align: justify;">Jari-jari (ruas garis OA, OB, OC, OD).</li>
<li style="text-align: justify;">Diameter (ruas garis AB)</li>
<li style="text-align: justify;">Tali Busur (ruas garis AD dan AB)</li>
<li style="text-align: justify;">Busur (garis lengkung AD, DC, AB)</li>
<li style="text-align: justify;">Juring (daerah BOC)</li>
<li style="text-align: justify;">Tembereng (daerah warna biru)</li>
<li style="text-align: justify;">Apotema (ruas garis OE)</li>
</ul>
<p> </p>
<p style="text-align: justify;">Nah, kalau kamu udah inget tentang masing-masing perbedaan unsur-unsur lingkaran tersebut, sekarang kita akan lanjut mencari tahu tentang cara menghitung unsur-unsur lingkaran. Simak baik-baik ya!</p>
<p style="text-align: justify;"><strong>Baca Juga: <a href="https://www.ruangguru.com/blog/pengertian-sifat-dan-rumus-kubus">Rumus Luas dan Volume Kubus serta Contoh Soal</a></strong></p>
<p> </p>
<h2><span style="font-size: 18pt;">1. Rumus Keliling dan Luas Lingkaran</span></h2>
<p style="text-align: justify;">Apa bedanya keliling lingkaran dan luas lingkaran? <strong>Keliling lingkaran</strong> adalah <strong>panjang garis lengkung dari suatu lingkaran</strong>, sedangkan <strong>luas lingkaran</strong> merupakan <strong>luas daerah yang dibatasi oleh busur lingkaran atau keliling lingkaran</strong>.</p>
<p style="text-align: justify;">Berikut rumus untuk menghitung keliling dan luas lingkaran.</p>
<p><img decoding="async" style="width: 609px; height: auto; max-width: 100%; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Feb-23-2023-05-32-35-3193-AM.png" alt="rumus keliling dan luas lingkaran" width="609" height="197" /></p>
<p> </p>
<p><strong>Contoh Soal!</strong></p>
<p style="text-align: justify;">1. Diketahui lingkaran dengan jari-jari 20 cm, keliling lingkaran tersebut adalah …</p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Diketahui: r = 20 cm</p>
<p style="text-align: justify;">Ditanya: Keliling lingkaran (K) …?</p>
<p> </p>
<p style="text-align: justify;"><strong>Jawab:</strong></p>
<p style="text-align: justify;">K = 2 × π × r<br />
K = 2 × 3,14 × 20<br />
K = 125,6 cm</p>
<p>Jadi, keliling lingkaran tersebut adalah 125,6 cm.</p>
<p> </p>
<p style="text-align: justify;">2. Jika diketahui sebuah lingkaran mempunyai diameter 10 cm. Berapakah luas lingkaran tersebut?</p>
<p><strong>Pembahasan:</strong></p>
<p>Diketahui: d = 10 cm</p>
<p>Ditanya: Luas lingkaran (L) …?</p>
<p> </p>
<p><strong>Jawab:</strong></p>
<p>L = 1/4 × π × d<sup>2</sup><br />
L = (1/4) × 3,14 × (10)<sup>2</sup><br />
L = (1/4) × 314<br />
L = 78,5 cm<sup>2</sup></p>
<p>Jadi, luas lingkaran tersebut adalah 78,5 cm<sup>2</sup>.</p>
<p> </p>
<h2><span style="font-size: 18pt;">2. Rumus Menghitung Sudut Pusat dan Sudut Keliling</span></h2>
<p style="text-align: justify;"><em>Ngejar Si Mamat makin bikin pusing (Tjakeeeep~~~)</em></p>
<p style="text-align: justify;"><em>Yuk, belajar sudut pusat dan sudut keliling.</em></p>
<p style="text-align: justify;">Sama-sama sudut yang ada di lingkaran tapi mereka berdua beda. Kadang kalau ga paham konsep, bisa bingung bedain keduanya. Tapi <em>santuy</em>, bareng Ruangguru, kamu jadi bisa ngebedain antara sudut pusat dan sudut keliling. Perhatiin deh pengertiannya sama gambarnya.</p>
<p style="text-align: justify;"><span style="color: #000000;"> </span></p>
<p><span style="color: #000000;"><img decoding="async" style="width: 244px; height: auto; max-width: 100%; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Feb-23-2023-05-34-12-2450-AM.png" alt="busur lingkaran" width="244" height="250" /></span></p>
<p style="text-align: center;"><em>(sumber: Video Belajar Ruangguru)</em></p>
<p> </p>
<p style="text-align: justify;"><strong>Sudut pusat</strong> itu merupakan <strong>daerah sudut yang dibatasi</strong> oleh <strong>dua jari-jari</strong> <strong>lingkaran</strong> yang <strong>titik sudutnya merupakan titik pusat lingkaran</strong>. Contoh: <strong><span style="color: #202124;">∠</span></strong><span style="color: #202124;">AOB.</span></p>
<p style="text-align: justify;">Nah, kalau<strong> sudut keliling</strong> merupakan <strong>daerah sudut yang dibatasi oleh dua tali busur yang berpotongan di satu titik</strong> pada lingkaran dan <strong>titik sudutnya terletak pada keliling lingkaran</strong>. Contoh: ∠ADB dan ∠ACB.</p>
<p style="text-align: justify;">Udah tau bedanya?</p>
<p style="text-align: justify;">Oke walaupun mereka beda, tapi mereka tuh nggak putus hubungan ya.</p>
<p style="text-align: justify;">Ada hubungan antara sudut pusat dan sudut keliling lingkaran.</p>
<p style="text-align: justify;">Kalau keduanya menghadap busur yang sama maka besar sudut pusat bakal sama dengan dua kalinya besar sudut keliling.</p>
<p style="text-align: justify;"><strong>Baca Juga: <a href="/blog/kedudukan-titik-dan-garis-lurus-terhadap-lingkaran" target="_blank" rel="noopener">Kedudukan Titik dan Garis Lurus terhadap Lingkaran</a></strong></p>
<p style="text-align: justify;"><span style="color: #000000;"><img loading="lazy" decoding="async" style="width: 451px; height: auto; max-width: 100%; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Feb-23-2023-05-35-34-7685-AM.png" alt="hubungan sudut pusat dan sudut keliling" width="451" height="177" /></span></p>
<p> </p>
<p style="text-align: justify;">Oh ya, biar kamu makin kenal sama sudut keliling, ga ada salahnya kamu pelajari sifat dari sudut keliling yaa biar jadi bestiie!</p>
<p> </p>
<h3 style="text-align: justify;"><span style="font-size: 14pt;">a. Besar sudut keliling yang menghadap diameter lingkaran adalah 90°</span></h3>
<p><span style="color: #000000;"><span style="color: #434856;"><img loading="lazy" decoding="async" style="width: 334px; height: auto; max-width: 100%; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Feb-23-2023-05-37-27-0852-AM.png" alt="besar sudut keliling yang menghadap diameter lingkaran" width="334" height="239" /></span></span></p>
<p style="text-align: center;"><em>(sumber: Video Belajar Ruangguru)</em></p>
<p> </p>
<h3 style="text-align: justify;"><span style="font-size: 14pt;">b. Besar sudut-sudut keliling yang menghadap busur yang sama adalah sama besar</span></h3>
<p><span style="color: #000000;"><img loading="lazy" decoding="async" style="width: 320px; height: auto; max-width: 100%; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Feb-23-2023-05-39-19-4891-AM.png" width="320" height="285" /></span></p>
<p style="text-align: center;"><em>(sumber: Video Belajar Ruangguru)</em></p>
<p> </p>
<h3 style="text-align: justify;"><span style="font-size: 14pt;">c. Jumlah besar sudut-sudut yang berhadapan pada segi empat tali busur (Segi empat yang sisinya tali busur) adalah 180°</span></h3>
<p><span style="color: #000000;"><img loading="lazy" decoding="async" style="width: 308px; height: auto; max-width: 100%; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Feb-23-2023-05-42-18-1612-AM.png" width="308" height="321" /></span></p>
<p style="text-align: center;"><em>(sumber: Video Belajar Ruangguru)</em></p>
<p> </p>
<p><strong>Contoh Soal!</strong></p>
<p style="text-align: justify;">Sebuah lingkaran memiliki besar ∠ABC = 60° dan ∠AOC = (4x – 12)°. Berapakah nilai x pada lingkaran tersebut?</p>
<p><strong>Pembahasan:</strong></p>
<p>Diketahui:</p>
<p>Sudut keliling lingkaran = ∠ABC = 60°</p>
<p>Sudut pusat lingkaran = ∠AOC = (4x – 12)°</p>
<p>Ditanya: Nilai x …?</p>
<p> </p>
<p><strong>Jawab:</strong></p>
<p>∠AOC = 2 × ∠ABC<br />
(4x – 12)° = 2 × 60°<br />
(4x – 12)° = 120°<br />
4x = 120° + 12°<br />
4x = 132°<br />
x = 33°</p>
<p>Jadi, didapat nilai x-nya adalah 33º. Sehingga, kita bisa tahu juga nih nilai sudut pusat lingkaran tersebut, yaitu:</p>
<p>∠AOC = (4x – 12)°<br />
∠AOC = (4(33) – 12)°<br />
∠AOC = (132 – 12)° = 120°</p>
<p>Berdasarkan perhitungan di atas, didapat nilai ∠AOC = 120°</p>
<p> </p>
<h2><span style="font-size: 18pt;">3. Rumus Panjang Busur dan Luas Juring</span></h2>
<p style="text-align: justify;">Busur dalam lingkaran itu bukan seperti busur yang digunakan untuk memanah ya <em>guys</em>.</p>
<p style="text-align: justify;">Busur bukan juga istri dari Pak Sur, hehehe.</p>
<p style="text-align: justify;">Dalam matematika, busur adalah <span style="font-weight: bold;">garis lengkung yang terletak pada lengkungan lingkaran dan menghubungkan dua titik pada keliling lingkaran</span>. Contohnya garis lengkung AB.</p>
<p style="text-align: justify;"><img loading="lazy" decoding="async" style="width: 232px; height: auto; max-width: 100%; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Feb-23-2023-05-44-30-4238-AM.png" alt="busur lingkaran" width="232" height="236" /></p>
<p style="text-align: center;"><em>(sumber: Video Belajar Ruangguru)</em></p>
<p> </p>
<p>Nah kalau juring itu daerah di dalem lingkaran yang dibatasi oleh dua jari-jari dan satu busur lingkaran. Contohnya luas juring AOB.</p>
<p style="text-align: justify;">Perlu kamu ketahui nih, buat cari panjang suatu busur dan luas juring, ada kaitannya sama sudut pusat lingkaran yang udah kamu pelajari di awal. Jangan kamu lupain ya.</p>
<p style="text-align: justify;">Untuk mencari panjang busur lingkaran, kamu bisa dapetin dengan konsep perbandingan antara besar sudut pusat yang menghadap busur dan panjang busur dibanding dengan besar sudut lingkaran dan panjang keliling lingkaran. Konsepnya kalau disederhanakan langsung kaya gini nih.</p>
<p style="text-align: justify;"><img loading="lazy" decoding="async" style="width: 422px; height: auto; max-width: 100%; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Feb-23-2023-05-45-34-0626-AM.png" alt="panjang busur" width="422" height="131" /></p>
<p> </p>
<p style="text-align: justify;">Sementara untuk mendapatkan luas juring, kamu bisa menggunakan konsep perbandingan antara besar sudut pusat yang menghadap busur dan luas juring yang dibatasi busur, dibanding dengan besar sudut lingkaran dan luas lingkaran. Rumusnya jadi seperti ini:</p>
<p style="text-align: justify; font-size: 16px;"><span style="color: #434856;"><img loading="lazy" decoding="async" style="width: 426px; height: auto; max-width: 100%; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Feb-23-2023-05-47-10-0173-AM.png" alt="luas juring" width="426" height="134" /></span></p>
<p> </p>
<p style="text-align: justify;">Dari dua konsep panjang busur dan luas juring di atas, kamu bisa membuat hubungan spesial dari keduanya yang bisa bantu kamu menyelesaikan suatu masalah.</p>
<p style="text-align: justify;">Kalau misal diketahui busur dan juringnya punya sudut pusat yang sama, terus ditanyakan salah satunya, kamu tinggal selesaikan menggunakan konsep perbandingan kaya gini.</p>
<p><strong>Baca Juga: <a href="/blog/matematika-kelas-8-3-cara-mencari-kemiringan-garis-lurus" target="_blank" rel="noopener">Cara Mencari Kemiringan (Gradien) pada Garis Lurus</a></strong></p>
<p style="text-align: justify;"><img loading="lazy" decoding="async" style="width: 412px; height: auto; max-width: 100%; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Feb-23-2023-05-47-51-2719-AM.png" alt="hubungan panjang busur dan luas juring" width="412" height="136" /></p>
<p> </p>
<p style="text-align: justify; font-size: 16px;"><span style="color: #434856;">Tapi kalau misalnya busur atau juringnya punya sudut yang berbeda, kamu juga bisa tetap menggunakan konsep perbandingan dengan membandingkan sudut pusat yang diketahui.</span></p>
<p style="text-align: justify; font-size: 16px;"><span style="color: #434856;"><img decoding="async" class="aligncenter" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Feb-23-2023-05-48-43-4313-AM.png" /></span></p>
<p style="text-align: center;"><em>(sumber: Video Belajar Ruangguru)</em></p>
<p> </p>
<h2><span style="font-size: 18pt;">4. Rumus Luas Tembereng</span></h2>
<p>Apa itu tembereng?</p>
<p style="text-align: justify;">Tembereng adalah <strong>daerah yang dibatasi oleh tali busur dan busur lingkaran</strong>. Dari gambar di atas, temberengnya adalah daerah yang berwarna biru.</p>
<p style="text-align: justify;">Kalau mau cari luas tembereng, sebenarnya itu guampang pol, kalau udah diketahui luas juring dan luas segitiga. Karena kalau kamu liat lagi gambarnya tuh, luas daerah tembereng AD itu sama kaya luas juring di atasnya, yaitu luas juring AOD yang dikurangi luas segitiga AOD.</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Feb-23-2023-05-49-37-3348-AM.png" /></p>
<p> </p>
<p style="text-align: justify;">Nah, itu tadi penjelasan lengkap mengenai cara menghitung unsur-unsur lingkaran. Semoga kamu semakin paham yah! Kalau kamu pengen tambah ngerti penjelasan dalam artikel ini, gabung yuk di <strong><a href="https://www.ruangguru.com/ruangbelajar">ruangbelajar</a></strong>.</p>
<p style="text-align: justify;">Ada banyak video belajar pake animasi, rangkuman kece, latian soal yang mudah sampe menantang, dan bahkan ada game nya juga yang bisa bikin kamu cinta buat belajar.</p>
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<p style="text-align: left;"><strong><span style="background-color: transparent;">Referensi:</span></strong></p>
<p>Raharjo M, Setiawan A. (2018) Matematika SMP/MTs Kelas VIII. Jakarta: Erlangga</p>
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<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">
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<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">
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<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">
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<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">
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<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>
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</picture>
</a>
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</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>
<div id="__next"></div>
<script type="speculationrules">
{"prefetch":[{"source":"document","where":{"and":[{"href_matches":"\/blog\/*"},{"not":{"href_matches":["\/blog\/wp-*.php","\/blog\/wp-admin\/*","\/blog\/wp-content\/uploads\/*","\/blog\/wp-content\/*","\/blog\/wp-content\/plugins\/*","\/blog\/wp-content\/themes\/ruangguru\/*","\/blog\/*\\?(.+)"]}},{"not":{"selector_matches":"a[rel~=\"nofollow\"]"}},{"not":{"selector_matches":".no-prefetch, .no-prefetch a"}}]},"eagerness":"conservative"}]}
</script>
<script>
async function getCtaDetails(ctaIds) {
const endpoint =
" https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/CTA/views/CTA?offset=0&limit=10&where=(ctaId,in," + ctaIds.toString() + ")";
try {
const response = await fetch(endpoint, {
headers: {
"xc-token": "-hG2nBDJzSj0agSgNtcJx97M4F02y54nUMoY6plJ",
},
});
const data = await response.json();
const ctaList = data?.list || [];
const ctaMap = new Map();
for (const ctaData of ctaList) {
ctaMap.set(ctaData.ctaId, ctaData);
}
return ctaMap;
} catch (error) {
console.error("Error fetching CTA details:", error);
return new Map();
}
}
async function replaceCTA() {
const regex = /{{cta\((‘(.*?)’|“(.*?)”)\)}}/g;
const bodyHTML = document.body.innerHTML;
const matches = Array.from(bodyHTML.matchAll(regex));
const ctaIds = matches.map((match) => {
let ctaId = match[2] ?? match[3];
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;">
<img src="${ctaData.imageUrl}" loading="lazy" alt="${ctaData.altText}" />
</a>`;
} else {
return match;
}
});
document.body.innerHTML = replacedHTML;
}
</script>
<meta name="author" content="Ruangguru Tech Team">
<!-- Google Tag Manager (noscript) -->
<noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-PVNLZFT" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>
<!-- Tracker -->
<script type="text/javascript" src="https://cdn-web-2.ruangguru.com/landing-page-web/public/staticpages/global-assets/js/cta.js"></script>
<script src="https://unpkg.com/@dotlottie/player-component@latest/dist/dotlottie-player.mjs" type="module"></script>
</body>
</html>