Perimeter of Quadrilateral

Perimeter of a Quadrilateral is the sum of all the sides of a perimeter. Suppose we are given a quadrilateral ABCD with sides AB, BC, CD, and DA then its perimeter is AB + BC + CD + DA.

In this article, we will learn about the Perimeter of Quadrilateral Definition and Formulas for Perimeter of various Quadrilateral, Examples, and others in detail.

What is Perimeter of a Quadrilateral?

Perimeter of a quadrilateral is the measure of its boundary. If you connect all four sides to create a single line, the length of that line is the perimeter. It’s measured in the same units as the sides, like meters, inches, or centimeters. So, if a side is measured in meters, the perimeter is also in meters.

Perimeter of a quadrilateral is the total length of its boundary.

It is found by adding up the lengths of all four sides. If a quadrilateral has sides labelled as AB, BC, CD, and DA, the perimeter is the sum of these lengths: AB + BC + CD + DA.

Perimeter of Quadrilateral Formula

The formula for finding the perimeter of a quadrilateral is simple: add up the lengths of all four sides. If the quadrilateral has sides labeled as AB, BC, CD, and DA, the perimeter (P) is calculated using the formula:

P = AB + BC + CD + DA

For example in a quadrilateral with 4 sides,

• AB = 4 units
• BC = 3 units
• CD = 5 units
• AD = 2 units

Perimeter (P) can be calculated by adding up the length of all the four sides as: AB + BC + CD + AD

P = 4+3+5+2 = 14 units

Perimeter of Different Types of Quadrilateral

In the given below table the formula for the perimeter of square, rectangle, rhombubs, parallelogram, kite and trapezoid are given. The image added below shows the different types of quadrilateral.

Although the formula will look same as they are all quadrilaterals and the sum of the sides is the perimeter. The table added below shows perimeter formula of some common quadrilateral.

Formula of Perimeter of Quadrilateral
Quadrilateral	Perimeter Formula
Square	4 × Side Length
Rectangle	2 × (Length + Width)
Parallelogram	2 × (Length + Width)
Rhombus	4 × Side Length
Kite	Sum of All four sides
Trapezoid	Sum of All four sides

Read More,

• Perimeter of Square

• Perimeter of Rectangle

• Perimeter of Parallelogram

• Perimeter of Rhombus

Perimeter of Quadrilateral with Inscribed Circle

For a quadrilateral with a circle inscribed (meaning the circle is tangent to all four sides of the quadrilateral), the perimeter (P) can be expressed using the lengths of the sides. Let’s denote the lengths of the sides as a, b, c, and d. The formula for the perimeter is:

P = a + b + c + d

The circle inscribed in a quadrilateral does not directly affect the perimeter of the quadrilateral but the properties of inscribed circle might be used to establish the relation between the side length to calculate the perimeter. Suppose we have a quadrilateral ABCD in which a circle is inscribed and the lines of the quadrilateral touches the circle at points P, Q, R, and S repectively then its area is given by,

Now to find the perimeter of quadrilateral ABCD we break it as,

Perimeter of ABCD = AB + BC + CD + DA

Perimeter of ABCD = AP + PB + BQ + QC + CR + RD + DS + SA…(i)

Now using Tangents Theorems we can say that,

• AP = AS
• BP = BQ
• CQ = CR
• DR = DS

from (i)

Perimeter of ABCD = AP + BQ + BQ + CQ + CQ + DS + DS + AP

Perimeter of ABCD = 2(AP + BQ + CQ + DS)

from the figure,

• AP = 5 cm
• BQ = 2 cm
• CQ = 6 cm
• DS = 1 cm

Perimeter of ABCD = 2(5 + 2 + 6 + 1)

Perimeter of ABCD = 2(14) = 28 cm

Perimeter of Cyclic Quadrilateral

A cyclic quadrilateral is a four-sided figure whose vertices all lie on the circumference of a single circle. In simpler terms, you can draw a circle passing through all four vertices of the quadrilateral.

P = a + b + c + d

where, a, b, c and d are sides of cyclic quadrilateral.

Similar to a quadrilateral with a circle inscribed, the presence of a circumscribed circle (a circle that goes through all vertices) doesn’t directly alter the perimeter formula. The cyclic property may be used to establish relationships between angles, but the calculation of the perimeter remains the sum of the lengths of the four sides.

Perimeter of Quadrilateral with Coordinates

For a quadrilateral defined by its coordinates in a coordinate plane, you can calculate the perimeter (P) using the distance formula between consecutive pairs of vertices. Let’s denote the coordinates of the vertices as (x₁, y₁), (x₂, y₂), (x₃, y₃), and (x₄, y₂). The distance between two points (x₁, y₁) and (x₂, y₂) is given by:

Perimeter is the sum of the distances between consecutive vertices:

P = Distance (V₁ and V₂) + Distance (V₂ and V₃) + Distance (V₃ and V₄) + Distance (V₄ and V₁)

In simple terms, you calculate the distance between each pair of consecutive vertices and then add up these distances to find the perimeter of the quadrilateral.

Examples of Perimeter of Quadrilateral

Example 1: A kite-shaped kite has two adjacent sides of 15 meters each and the other two sides of 10 meters each. What is the perimeter of the kite?

Solution:

Given,

• Two adjacent sides of the kite, a = 15 meters
• Other two sides of the kite, b = 10 meters

Formula for Perimeter (P) of a kite is P = 2 × (a + b)

Substitute the given values:

P = 2 × (15 + 10)

Calculate the expression inside the parentheses:

P = 2 × 25

P = 50

So, the perimeter of the kite is 50 meters.

Example 2: A rhombus has diagonals measuring 16 units and 30 units. Calculate the perimeter of the rhombus.

Solution:

Given:

• Length of one diagonal, d₁ = 16 units
• Length of the other diagonal, d₂ = 30 units

In a rhombus, the diagonals bisect each other at right angles. The formula for the side length (s) in terms of the diagonals is

Substitute the given values:

Calculate the expression inside the square root:

Combine the terms inside the square root:

s = 17

The perimeter (P) of a rhombus is given by P = 4s.

Substitute the calculated side length:

P = 4 ×17

P = 68

So, the perimeter of the rhombus is 68 units.

Example 3: A cyclic quadrilateral ABCD has sides of lengths 6, 8, 10, and 12 units. Calculate the perimeter of the cyclic quadrilateral.

Solution:

Given:

• Side lengths of Cyclic Quadrilateral: a = 6, b = 8, c = 10, d = 12

Perimeter (P) of a cyclic quadrilateral is simply the sum of its side lengths: P = a + b + c + d

Substitute the given values:

P = 6 + 8 + 10 + 12

P = 36

So, Perimeter of the cyclic quadrilateral is 36 units.

Example 4: Trapezoid LMNO has bases LM and NO with lengths 15 units and 10 units, respectively. The non-parallel sides have lengths 8 units each. Determine the perimeter of trapezoid LMNO.

Solution:

Given,

• Length of base LM, a = 15 units
• Length of base NO, b = 10 units
• Length of non-parallel sides, c = d = 8 units

Formula for Perimeter (P) of a trapezoid is P = a + b + c + d

Substitute the given values:

P = 15 + 10 + 8 + 8

P = 41

So, the perimeter of trapezoid LMNO is 41 units.

Perimeter of Quadrilateral – Practice Questions

Q1. Rectangle ABCD has a length of 12 units and a width of 8 units. Find the perimeter of the rectangle.

Q2. A square has a side length of 15 centimeters. Calculate the perimeter of the square.

Q3. In a parallelogram PQRS, opposite sides PQ and SR have lengths 20 units and 14 units, respectively. Find the perimeter of the parallelogram.

Q4. A rhombus has side lengths of 18 units each. Determine the perimeter of the rhombus.

Q5. A kite-shaped kite has two adjacent sides of 25 meters each and the other two sides of 18 meters each. What is the perimeter of the kite?

Q6. A cyclic quadrilateral ABCD has sides of lengths 8, 15, 18, and 25 units. Calculate the perimeter of the cyclic quadrilateral.

Perimeter of Quadrilateral – FAQs

1. What is Formula of Perimeter of Quadrilateral?

The formula for finding the perimeter (P) of a quadrilateral is given as the sum of the lengths of all four sides: P=a+b+c+d, where a,b,c, and d represent the lengths of the individual sides.

2. How to Find Perimeter of a Quadrilateral With Coordinates?

To find the perimeter of a quadrilateral with coordinates, use the distance formula between consecutive vertices. Add up the distances between each pair of adjacent vertices to obtain the total perimeter.

3. What is Perimeter of a Convex Quadrilateral?

For any complex quadrilateral with sides a, b, c, and d we can easily calculates its perimeter by adding all its sides.

4. How to Find Perimeter of Quadrilateral?

To find the Perimeter of Quadrilateral, add the length of four sides of the quadrilateral

5. What is Quadrilateral?

Quadrilateral is a Polygon bounded by four line segments