Perimeter of Cyclic Quadrilateral
2026-02-28 01:10 Diff
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Last updated on September 8, 2025

The perimeter of a shape is the total length of its boundary. The sum of all four sides is called the perimeter of a cyclic quadrilateral. Perimeter is also used for fencing a property, sewing, and more. In this topic, we will learn about the perimeter of a cyclic quadrilateral.

What is the Perimeter of a Cyclic Quadrilateral?

The perimeter of a cyclic quadrilateral is the total length of its four sides. By adding the length of all four sides, we get the perimeter of the shape.

The formula for the perimeter of a cyclic quadrilateral is 𝑃 = 𝑎 + 𝑏 + 𝑐 + 𝑑, where a, b, c, and d are the sides of the quadrilateral.

For instance, if a cyclic quadrilateral has sides, a = 5, b = 7, c = 9, and d = 11, then its perimeter is P = 5 + 7 + 9 + 11 = 32.

Formula for Perimeter of Cyclic Quadrilateral - 𝑃 = 𝑎 + 𝑏 + 𝑐 + 𝑑.

Let’s consider another example of a cyclic quadrilateral with side lengths, 𝑎 = 6, 𝑏 = 8, 𝑐 = 10, and 𝑑 = 12.

So the perimeter of the quadrilateral will be: 𝑃 = 𝑎 + 𝑏 + 𝑐 + 𝑑 = 6 + 8 + 10 + 12 = 36.

How to Calculate the Perimeter of a Cyclic Quadrilateral

To find the perimeter of a cyclic quadrilateral, we just need to apply the given formula and sum all the sides of the quadrilateral. For instance, a given cyclic quadrilateral has sides of a = 8, b = 8, c = 8, d = 8. Perimeter = sum of all sides = 8 + 8 + 8 + 8 = 32 cm.

Example Problem on Perimeter of Cyclic Quadrilateral -

For finding the perimeter of a cyclic quadrilateral, we use the formula, 𝑃 = 𝑎 + 𝑏 + 𝑐 + 𝑑.

For example, let’s say, a = 4 cm, b = 5 cm, c = 6 cm, and d = 7 cm.

Now, the perimeter = sum of all sides = 4 + 5 + 6 + 7 = 22 cm. Therefore, the perimeter of the cyclic quadrilateral is 22 cm.

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Tips and Tricks for Perimeter of Cyclic Quadrilateral

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

  • Always remember that a cyclic quadrilateral's perimeter is simply the sum of the four sides of the shape. For that, use the formula, 𝑃 = 𝑎 + 𝑏 + 𝑐 + 𝑑. Calculating the perimeter of a cyclic quadrilateral starts by determining the length of each side using the distance formula.
  • The distance formula is: Distance = √((x₂-x₁)² + (y₂-y₁)²). Here, (x₁, y₁) and (x₂, y₂) indicate the positions of two points that make up a quadrilateral’s side. They can be found by adding the lengths of four sides after they are calculated.
  • To reduce confusion, specifically, arrange the indicated side lengths if you need the perimeter of a group of cyclic quadrilaterals.
  • After that, apply the formula to each quadrilateral. To avoid mistakes when adding the perimeter, make sure the side lengths are precise and constant for common uses like gardening and architecture.
  • If you are given the semi-perimeter, which is half the perimeter, you can multiply it by 2 to determine the full perimeter. Area-related calculations, like Brahmagupta’s formula, often use the semi-perimeter.

Common Mistakes and How to Avoid Them in Perimeter of Cyclic Quadrilateral

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

Problem 1

A garden is shaped like a cyclic quadrilateral with a perimeter of 50 meters. Three sides measure 12 meters, 15 meters, and 10 meters. To find out the missing side, subtract the sum of the known sides from the total perimeter.

Okay, lets begin

Length of the missing side = 13 meters.

Explanation

Let ‘d’ be the length of the missing side. And the given perimeter = 50 meters. Length of the three sides = 12 meters, 15 meters, and 10 meters. Perimeter of the cyclic quadrilateral = sum of lengths of four sides. 50 = 12 + 15 + 10 + d 50 = 37 + d d = 50 – 37 = 13 Therefore, the missing side is 13 meters.

Well explained 👍

Problem 2

A piece of wire with a perimeter of 120 inches is reshaped into a cyclic quadrilateral with equal sides. Find the length of each side of the quadrilateral by dividing the total length by 4.

Okay, lets begin

30 inches

Explanation

Given that the perimeter of the wire is equal to the total length of the cyclic quadrilateral, here is the solution: Perimeter of the wire = Total length of the quadrilateral Length of the wire used = Perimeter of the quadrilateral formed Perimeter of an equilateral quadrilateral = 4 × a 120 = 4 × a 120 ÷ 4 = 30 a = 30 Therefore, the length of each side of the quadrilateral is 30 inches.

Well explained 👍

Problem 3

Find the perimeter of a cyclic quadrilateral whose sides are 8 cm, 9 cm, 7 cm, and 6 cm.

Okay, lets begin

30 cm

Explanation

Perimeter of quadrilateral = a + b + c + d P = 8 + 9 + 7 + 6 = 30 Therefore, the perimeter of the quadrilateral is 30 cm.

Well explained 👍

Problem 4

Mike has a cyclic quadrilateral-shaped patio in his backyard. He measures the four sides of the patio: Side A = 14 meters Side B = 12 meters Side C = 10 meters Side D = 8 meters How much fencing should Mike buy to go around the edge of the patio?

Okay, lets begin

Mike will need 44 meters of fencing to go around the patio.

Explanation

The perimeter of a cyclic quadrilateral is the sum of all the four sides. Using the formula: P = a + b + c + d P = 14 + 12 + 10 + 8 = 44 meters.

Well explained 👍

Problem 5

Find the perimeter of a cyclic quadrilateral with sides a = 11, b = 9, c = 8, d = 10.

Okay, lets begin

Perimeter = a + b + c + d = 11 + 9 + 8 + 10 = 38 meters.

Explanation

Each side of the cyclic quadrilateral is summed to calculate the entire distance around the shape, which is 38 meters.

Well explained 👍

FAQs on Perimeter of Cyclic Quadrilateral

1.Evaluate the cyclic quadrilateral’s perimeter if its sides are 5 cm, 7 cm, 9 cm, and 4 cm.

Perimeter of cyclic quadrilateral = a + b + c + d, Hence P = 5 + 7 + 9 + 4 = 25 cm.

2.What is meant by a cyclic quadrilateral’s perimeter?

The total length around a cyclic quadrilateral’s sides is its perimeter. In other words, the perimeter of a cyclic quadrilateral is the total length of its sides.

3.What are the types of quadrilaterals?

There are several types of quadrilaterals: Square, Rectangle, Rhombus, Parallelogram, Trapezium, and Kite.

4.Which quadrilateral has all equal sides?

A rhombus is a quadrilateral with all sides equal in length.

5.Which quadrilateral has the smallest perimeter for a given area?

For a given area, the square has the smallest perimeter.

Important Glossaries for Perimeter of Cyclic Quadrilateral

  • Perimeter: The total length of the sides of a shape.
  • Cyclic Quadrilateral: A quadrilateral that can be inscribed in a circle.
  • Formula of perimeter: The mathematical expression used to calculate the perimeter of a cyclic quadrilateral is 𝑃 = 𝑎 + 𝑏 + 𝑐 + 𝑑.
  • Semi-perimeter: Half of the perimeter, often used in formulas related to area calculations.
  • Brahmagupta’s formula: A method to calculate the area of a cyclic quadrilateral using its semi-perimeter.

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Seyed Ali Fathima S

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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.

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