Perimeter of Quarter Circle
2026-02-21 21:10 Diff
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Last updated on December 28, 2025

The perimeter of a shape is the total length of its boundary. The perimeter of a quarter circle includes the curved part of the circle and the two radii. Perimeters are used in various applications like fencing, sewing, and more. In this topic, we will learn about the perimeter of a quarter circle.

What is the Perimeter of a Quarter Circle?

The perimeter of a quarter circle is the sum of the curved part of the circle and the two radii.

The formula for the perimeter of a quarter circle is \(( P = \frac{1}{4} \times 2\pi r + 2r ),\) where  r  is the radius of the circle

For example, if a quarter circle has a radius  r = 4 , then its perimeter is 

P =\( \frac{1}{4} \times 2 \times 3.14 \times 4 + 2 \times 4 = 6.28 + 8 = 14.28 .\)

Formula for Perimeter of Quarter Circle - \( P = \frac{1}{4} \times 2\pi r + 2r \).

Let’s consider another example of a quarter circle with a radius of  r = 5 .

So the perimeter of the quarter circle will be: \(( P = \frac{1}{4} \times 2\pi r + 2r = \frac{1}{4} \times 2 \times 3.14 \times 5 + 2 \times 5 = 7.85 + 10 = 17.85 ).\)

How to Calculate the Perimeter of a Quarter Circle

To find the perimeter of a quarter circle, apply the given formula by adding the curved part of the circle to the two radii.

For instance, given a quarter circle with a radius r = 6 , the perimeter =\( ( \frac{1}{4} \times 2\pi r + 2r = \frac{1}{4} \times 2 \times 3.14 \times 6 + 2 \times 6 = 9.42 + 12 = 21.42 ). \)

Example

Problem on Perimeter of Quarter Circle -

For finding the perimeter of a quarter circle, use the formula\( ( P = \frac{1}{4} \times 2\pi r + 2r ).\)

For example, let’s say the radius  r = 3 .

Now, the perimeter =\( ( \frac{1}{4} \times 2 \times 3.14 \times 3 + 2 \times 3 = 4.71 + 6 = 10.71 ).\) Therefore, the perimeter of the quarter circle is 10.71.

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Tips and Tricks for Perimeter of Quarter Circle

Learning some tips and tricks makes it easier for children to calculate the perimeter of quarter circles. Here are some tips and tricks given below:

  • Always remember that a quarter circle's perimeter is the sum of the curved part of the circle and the two radii. Use the formula\( ( P = \frac{1}{4} \times 2\pi r + 2r ).\)
  • Calculating the perimeter starts by determining the radius. Make sure to use the correct value of \\((pi),\) typically approximated as 3.14.
  • To avoid mistakes, ensure the radius is precise and consistent for applications like construction or crafting.
  • If you are given the diameter, divide it by 2 to find the radius before applying the formula to calculate the perimeter.
  • Make sure to thoroughly understand the concept of a quarter circle, which is a quarter of a full circle, including the curved edge and two straight sides (radii).

Common Mistakes and How to Avoid Them in Perimeter of Quarter Circle

Did you know that while working with the perimeter of a quarter circle, children might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:

Problem 1

A garden has a quarter circle boundary with a radius of 7 meters. Calculate the perimeter of this boundary.

Okay, lets begin

Perimeter of the quarter circle = 25.98 meters.

Explanation

Given radius r = 7  meter

Perimeter of quarter circle = \(( \frac{1}{4} \times 2\pi r + 2r = \frac{1}{4} \times 2 \times 3.14 \times 7 + 2 \times 7 = 10.99 + 14 = 25.98 ).\)

Well explained 👍

Problem 2

A quarter circle-shaped window has a perimeter of 18.85 inches. If the radius is 3 inches, verify the perimeter calculation.

Okay, lets begin

18.85 inches

Explanation

Given radius  r = 3  inches

Perimeter of quarter circle =\(( \frac{1}{4} \times 2\pi r + 2r = \frac{1}{4} \times 2 \times 3.14 \times 3 + 2 \times 3 = 4.71 + 6 = 10.71 ).\) However, since the measured perimeter is 18.85 inches, verify if additional elements were included in the measurement.

Well explained 👍

Problem 3

Find the perimeter of a quarter circle with a radius of 8 cm.

Okay, lets begin

25.12 cm

Explanation

Perimeter of quarter circle =\( ( \frac{1}{4} \times 2\pi r + 2r = \frac{1}{4} \times 2 \times 3.14 \times 8 + 2 \times 8 = 12.56 + 16 = 28.56 ).\)

Well explained 👍

Problem 4

A park has a quarter circle section with a radius of 12 meters. How much fencing is needed around this section?

Okay, lets begin

35.42 meters of fencing is needed.

Explanation

The perimeter of a quarter circle is the sum of the curved edge and the two radii. Using the formula:

\( ( P = \frac{1}{4} \times 2\pi r + 2r = \frac{1}{4} \times 2 \times 3.14 \times 12 + 2 \times 12 = 18.84 + 24 = 42.84 ).\)

Well explained 👍

Problem 5

Calculate the perimeter of a quarter circle with a radius of 15 meters.

Okay, lets begin

58.5 meters

Explanation

The perimeter calculation involves the curved section and the two radii:

\(( P = \frac{1}{4} \times 2\pi r + 2r = \frac{1}{4} \times 2 \times 3.14 \times 15 + 2 \times 15 = 23.55 + 30 = 53.55 )\).

Well explained 👍

FAQs on Perimeter of Quarter Circle

1.Evaluate the perimeter of a quarter circle if the radius is 10 cm.

Perimeter of quarter circle = \(( \frac{1}{4} \times 2\pi r + 2r = \frac{1}{4} \times 2 \times 3.14 \times 10 + 2 \times 10 = 15.7 + 20 = 35.7 ) cm.\)

2.What is meant by a quarter circle’s perimeter?

The total length around a quarter circle's curved edge and the two radii is its perimeter. It combines the arc length of the circle with the two radii.

3.What is the formula for the perimeter of a quarter circle?

The formula for the perimeter of a quarter circle is\( ( P = \frac{1}{4} \times 2\pi r + 2r ),\) where  r  is the radius.

4.How do you find the radius if given the diameter?

Divide the diameter by 2 to find the radius.

5.What is the significance of \(\pi\) in calculating the perimeter?

\((\pi)\) is a constant used to calculate the circumference of circles and arcs, essential for determining the curved part of the quarter circle's perimeter.

Important Glossaries for Perimeter of Quarter Circle

  • Perimeter: The total length of the boundary of a shape.
  • Quarter Circle: A section of a circle that represents one-fourth of the entire circle, including the arc and two radii.
  • Radius: The distance from the center of a circle to any point on its circumference.
  • Arc Length: The distance along the curved part of the circle.
  • \((\pi):\) A mathematical constant approximately equal to 3.14, used in calculations involving circles.

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Seyed Ali Fathima S

About the Author

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.

Fun Fact

: She has songs for each table which helps her to remember the tables