Perimeter of 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.

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.

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.

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.

• 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.