1 added
2 removed
Original
2026-01-01
Modified
2026-02-28
1
-
<p>317 Learners</p>
1
+
<p>394 Learners</p>
2
<p>Last updated on<strong>August 5, 2025</strong></p>
2
<p>Last updated on<strong>August 5, 2025</strong></p>
3
<p>The perimeter of a shape is the total length of its boundary. The perimeter of an arc refers to the length of the curved part of a circle, which can be used in designing structures, gardens, and more. In this topic, we will learn about the perimeter of an arc.</p>
3
<p>The perimeter of a shape is the total length of its boundary. The perimeter of an arc refers to the length of the curved part of a circle, which can be used in designing structures, gardens, and more. In this topic, we will learn about the perimeter of an arc.</p>
4
<h2>What is the Perimeter of an Arc?</h2>
4
<h2>What is the Perimeter of an Arc?</h2>
5
<p>The perimeter<a>of</a>an arc is the length of the curved boundary of a part of a circle. It is calculated as a<a>fraction</a>of the circumference of the circle, which is proportional to the angle that the arc subtends at the center of the circle. The<a>formula</a>for the perimeter of an arc is 𝑃 = 2πr(θ/360) + 2r, where r is the radius of the circle and θ is the angle in degrees. For instance, if a circle has a radius of 5 units and the arc subtends an angle of 60 degrees, then its perimeter is 𝑃 = 2π(5)(60/360) + 2(5) = 5π/3 + 10.</p>
5
<p>The perimeter<a>of</a>an arc is the length of the curved boundary of a part of a circle. It is calculated as a<a>fraction</a>of the circumference of the circle, which is proportional to the angle that the arc subtends at the center of the circle. The<a>formula</a>for the perimeter of an arc is 𝑃 = 2πr(θ/360) + 2r, where r is the radius of the circle and θ is the angle in degrees. For instance, if a circle has a radius of 5 units and the arc subtends an angle of 60 degrees, then its perimeter is 𝑃 = 2π(5)(60/360) + 2(5) = 5π/3 + 10.</p>
6
<h2>Formula for Perimeter of Arc - 𝑷 = 2πr(θ/360) + 2r.</h2>
6
<h2>Formula for Perimeter of Arc - 𝑷 = 2πr(θ/360) + 2r.</h2>
7
<p>Let’s consider another example of calculating the perimeter of an arc with a circle of radius 7 units and an angle of 90 degrees. The perimeter of the arc will be: 𝑃 = 2π(7)(90/360) + 2(7) = 7π/2 + 14.</p>
7
<p>Let’s consider another example of calculating the perimeter of an arc with a circle of radius 7 units and an angle of 90 degrees. The perimeter of the arc will be: 𝑃 = 2π(7)(90/360) + 2(7) = 7π/2 + 14.</p>
8
<h2>How to Calculate the Perimeter of an Arc</h2>
8
<h2>How to Calculate the Perimeter of an Arc</h2>
9
<p>To find the perimeter of an arc, apply the given formula and calculate both the arc length and the two radii. For instance, if a circle has a radius of 8 units and the arc subtends an angle of 45 degrees, then: Arc Length = 2π(8)(45/360) = π/2 Perimeter = Arc Length + 2(8) = π/2 + 16 units. Example Problem on Perimeter of Arc - For finding the perimeter of an arc, we use the formula, 𝑷 = 2πr(θ/360) + 2r. For example, let’s say, r = 6 units and θ = 120 degrees. Now, the perimeter = Arc Length + 2r = 2π(6)(120/360) + 2(6) = 4π + 12. Therefore, the perimeter of the arc is 4π + 12 units.</p>
9
<p>To find the perimeter of an arc, apply the given formula and calculate both the arc length and the two radii. For instance, if a circle has a radius of 8 units and the arc subtends an angle of 45 degrees, then: Arc Length = 2π(8)(45/360) = π/2 Perimeter = Arc Length + 2(8) = π/2 + 16 units. Example Problem on Perimeter of Arc - For finding the perimeter of an arc, we use the formula, 𝑷 = 2πr(θ/360) + 2r. For example, let’s say, r = 6 units and θ = 120 degrees. Now, the perimeter = Arc Length + 2r = 2π(6)(120/360) + 2(6) = 4π + 12. Therefore, the perimeter of the arc is 4π + 12 units.</p>
10
<h3>Explore Our Programs</h3>
10
<h3>Explore Our Programs</h3>
11
-
<p>No Courses Available</p>
12
<h2>Tips and Tricks for Perimeter of Arc</h2>
11
<h2>Tips and Tricks for Perimeter of Arc</h2>
13
<p>Learning some tips and tricks makes it easier for children to calculate the perimeter of arcs. Here are some tips and tricks given below: Always remember that an arc's perimeter involves both the arc length and the two radii of the circle. Use the formula, 𝑷 = 2πr(θ/360) + 2r. Calculating the arc length starts by determining the radius and the angle. Ensure the angle is in degrees for using the formula. To reduce confusion, arrange the given measurements clearly when dealing with<a>multiple</a>arcs. Apply the formula to each arc separately. To avoid mistakes when calculating the perimeter, ensure the radius and angle measurements are accurate and consistent, especially for practical uses like construction and decoration. If you are given the arc length and need to find the perimeter, remember to add twice the radius to the arc length.</p>
12
<p>Learning some tips and tricks makes it easier for children to calculate the perimeter of arcs. Here are some tips and tricks given below: Always remember that an arc's perimeter involves both the arc length and the two radii of the circle. Use the formula, 𝑷 = 2πr(θ/360) + 2r. Calculating the arc length starts by determining the radius and the angle. Ensure the angle is in degrees for using the formula. To reduce confusion, arrange the given measurements clearly when dealing with<a>multiple</a>arcs. Apply the formula to each arc separately. To avoid mistakes when calculating the perimeter, ensure the radius and angle measurements are accurate and consistent, especially for practical uses like construction and decoration. If you are given the arc length and need to find the perimeter, remember to add twice the radius to the arc length.</p>
14
<h2>Common Mistakes and How to Avoid Them in Perimeter of Arc</h2>
13
<h2>Common Mistakes and How to Avoid Them in Perimeter of Arc</h2>
15
<p>Did you know that while working with the perimeter of an arc, children might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:</p>
14
<p>Did you know that while working with the perimeter of an arc, children might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:</p>
16
<h3>Problem 1</h3>
15
<h3>Problem 1</h3>
17
<p>A circular garden has an arc with a perimeter of 40 units. The radius of the garden is 10 units, and the arc subtends an angle of 72 degrees. Calculate the arc length.</p>
16
<p>A circular garden has an arc with a perimeter of 40 units. The radius of the garden is 10 units, and the arc subtends an angle of 72 degrees. Calculate the arc length.</p>
18
<p>Okay, lets begin</p>
17
<p>Okay, lets begin</p>
19
<p>Arc Length = 12.57 units (approximately).</p>
18
<p>Arc Length = 12.57 units (approximately).</p>
20
<h3>Explanation</h3>
19
<h3>Explanation</h3>
21
<p>Let ‘L’ be the arc length. And the given perimeter = 40 units. Radius of the garden = 10 units. Perimeter of arc = Arc Length + 2(radius). 40 = L + 2(10) 40 = L + 20 L = 40 - 20 = 20 Therefore, the arc length is approximately 12.57 units.</p>
20
<p>Let ‘L’ be the arc length. And the given perimeter = 40 units. Radius of the garden = 10 units. Perimeter of arc = Arc Length + 2(radius). 40 = L + 2(10) 40 = L + 20 L = 40 - 20 = 20 Therefore, the arc length is approximately 12.57 units.</p>
22
<p>Well explained 👍</p>
21
<p>Well explained 👍</p>
23
<h3>Problem 2</h3>
22
<h3>Problem 2</h3>
24
<p>A wire of length 150 units is used to form an arc of a circle with a radius of 15 units. The arc subtends an angle of 180 degrees at the center. Find the perimeter of this arc.</p>
23
<p>A wire of length 150 units is used to form an arc of a circle with a radius of 15 units. The arc subtends an angle of 180 degrees at the center. Find the perimeter of this arc.</p>
25
<p>Okay, lets begin</p>
24
<p>Okay, lets begin</p>
26
<p>Perimeter = 60π + 30 units.</p>
25
<p>Perimeter = 60π + 30 units.</p>
27
<h3>Explanation</h3>
26
<h3>Explanation</h3>
28
<p>Given that the length of the wire forms the arc, the perimeter is calculated as: Arc Length = 2π(15)(180/360) = 15π Perimeter of arc = Arc Length + 2(radius) = 15π + 2(15) = 15π + 30 Therefore, the perimeter of the arc is 15π + 30 units.</p>
27
<p>Given that the length of the wire forms the arc, the perimeter is calculated as: Arc Length = 2π(15)(180/360) = 15π Perimeter of arc = Arc Length + 2(radius) = 15π + 2(15) = 15π + 30 Therefore, the perimeter of the arc is 15π + 30 units.</p>
29
<p>Well explained 👍</p>
28
<p>Well explained 👍</p>
30
<h3>Problem 3</h3>
29
<h3>Problem 3</h3>
31
<p>Find the perimeter of an arc of a circle with a radius of 5 units and an angle of 45 degrees.</p>
30
<p>Find the perimeter of an arc of a circle with a radius of 5 units and an angle of 45 degrees.</p>
32
<p>Okay, lets begin</p>
31
<p>Okay, lets begin</p>
33
<p>Perimeter = (5π/4) + 10 units.</p>
32
<p>Perimeter = (5π/4) + 10 units.</p>
34
<h3>Explanation</h3>
33
<h3>Explanation</h3>
35
<p>Perimeter of arc = Arc Length + 2(radius) = 2π(5)(45/360) + 2(5) = (5π/4) + 10 Therefore, the perimeter of the arc is (5π/4) + 10 units.</p>
34
<p>Perimeter of arc = Arc Length + 2(radius) = 2π(5)(45/360) + 2(5) = (5π/4) + 10 Therefore, the perimeter of the arc is (5π/4) + 10 units.</p>
36
<p>Well explained 👍</p>
35
<p>Well explained 👍</p>
37
<h3>Problem 4</h3>
36
<h3>Problem 4</h3>
38
<p>An artist is designing a circular mosaic with an arc. The circle has a radius of 12 units, and the arc subtends an angle of 60 degrees. How much material is needed to cover the perimeter of the arc?</p>
37
<p>An artist is designing a circular mosaic with an arc. The circle has a radius of 12 units, and the arc subtends an angle of 60 degrees. How much material is needed to cover the perimeter of the arc?</p>
39
<p>Okay, lets begin</p>
38
<p>Okay, lets begin</p>
40
<p>The artist will need 4π + 24 units of material.</p>
39
<p>The artist will need 4π + 24 units of material.</p>
41
<h3>Explanation</h3>
40
<h3>Explanation</h3>
42
<p>The perimeter of the arc includes the arc length and the two radii. Using the formula: Arc Length = 2π(12)(60/360) = 4π Perimeter = Arc Length + 2(radius) = 4π + 2(12) = 4π + 24 units.</p>
41
<p>The perimeter of the arc includes the arc length and the two radii. Using the formula: Arc Length = 2π(12)(60/360) = 4π Perimeter = Arc Length + 2(radius) = 4π + 2(12) = 4π + 24 units.</p>
43
<p>Well explained 👍</p>
42
<p>Well explained 👍</p>
44
<h3>Problem 5</h3>
43
<h3>Problem 5</h3>
45
<p>Find the perimeter of the arc of a circle with radius 9 units and an angle of 120 degrees.</p>
44
<p>Find the perimeter of the arc of a circle with radius 9 units and an angle of 120 degrees.</p>
46
<p>Okay, lets begin</p>
45
<p>Okay, lets begin</p>
47
<p>Perimeter = 3π + 18 units.</p>
46
<p>Perimeter = 3π + 18 units.</p>
48
<h3>Explanation</h3>
47
<h3>Explanation</h3>
49
<p>The perimeter of the arc includes the arc length and the two radii. The entire distance is calculated as: Arc Length = 2π(9)(120/360) = 3π Perimeter = Arc Length + 2(radius) = 3π + 18 units.</p>
48
<p>The perimeter of the arc includes the arc length and the two radii. The entire distance is calculated as: Arc Length = 2π(9)(120/360) = 3π Perimeter = Arc Length + 2(radius) = 3π + 18 units.</p>
50
<p>Well explained 👍</p>
49
<p>Well explained 👍</p>
51
<h2>FAQs on Perimeter of Arc</h2>
50
<h2>FAQs on Perimeter of Arc</h2>
52
<h3>1.Evaluate the arc’s perimeter if its radius is 6 units and the angle is 30 degrees.</h3>
51
<h3>1.Evaluate the arc’s perimeter if its radius is 6 units and the angle is 30 degrees.</h3>
53
<p>Perimeter of arc = Arc Length + 2(radius), Hence 𝑃 = π + 12 units.</p>
52
<p>Perimeter of arc = Arc Length + 2(radius), Hence 𝑃 = π + 12 units.</p>
54
<h3>2.What is meant by an arc’s perimeter?</h3>
53
<h3>2.What is meant by an arc’s perimeter?</h3>
55
<p>The total length around the arc’s curved boundary plus the two radii is its perimeter. In other words, the perimeter of an arc is the<a>sum</a>of the arc length and twice the radius.</p>
54
<p>The total length around the arc’s curved boundary plus the two radii is its perimeter. In other words, the perimeter of an arc is the<a>sum</a>of the arc length and twice the radius.</p>
56
<h3>3.What are the types of arcs?</h3>
55
<h3>3.What are the types of arcs?</h3>
57
<p>There are two main types of arcs:<a>minor</a>arcs, which are<a>less than</a>a semicircle, and major arcs, which are more than a semicircle.</p>
56
<p>There are two main types of arcs:<a>minor</a>arcs, which are<a>less than</a>a semicircle, and major arcs, which are more than a semicircle.</p>
58
<h3>4.Which arc represents half the circle?</h3>
57
<h3>4.Which arc represents half the circle?</h3>
59
<p>A semicircular arc represents half the circle.</p>
58
<p>A semicircular arc represents half the circle.</p>
60
<h3>5.Which angle results in the smallest arc?</h3>
59
<h3>5.Which angle results in the smallest arc?</h3>
61
<p>An angle close to 0 degrees results in the smallest arc.</p>
60
<p>An angle close to 0 degrees results in the smallest arc.</p>
62
<h2>Important Glossaries for Perimeter of Arc</h2>
61
<h2>Important Glossaries for Perimeter of Arc</h2>
63
<p>Arc: A part of the circumference of a circle. Radius: The distance from the center of a circle to any point on its boundary. Angle: The measure in degrees of the circle's sector that the arc spans. Circumference: The total length around a circle. Perimeter of Arc: The sum of the arc length and twice the radius.</p>
62
<p>Arc: A part of the circumference of a circle. Radius: The distance from the center of a circle to any point on its boundary. Angle: The measure in degrees of the circle's sector that the arc spans. Circumference: The total length around a circle. Perimeter of Arc: The sum of the arc length and twice the radius.</p>
64
<p>What Is Measurement? 📏 | Easy Tricks, Units & 🎯 Fun Learning for Kids | ✨BrightCHAMPS Math</p>
63
<p>What Is Measurement? 📏 | Easy Tricks, Units & 🎯 Fun Learning for Kids | ✨BrightCHAMPS Math</p>
65
<p>▶</p>
64
<p>▶</p>
66
<h2>Seyed Ali Fathima S</h2>
65
<h2>Seyed Ali Fathima S</h2>
67
<h3>About the Author</h3>
66
<h3>About the Author</h3>
68
<p>Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.</p>
67
<p>Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.</p>
69
<h3>Fun Fact</h3>
68
<h3>Fun Fact</h3>
70
<p>: She has songs for each table which helps her to remember the tables</p>
69
<p>: She has songs for each table which helps her to remember the tables</p>