Created By : Abhinandan Kumar

Reviewed By : Rajashekhar Valipishetty

Last Updated : Apr 24, 2023

Area of an Irregular Quadrilateral Calculator: Are you looking for any help while solving the geometry exercises of any class? Then you are on the right place. This page gives the complete details regarding area of an irregular quadrilateral. You can get the information like what is meant by irregular quadrilateral area, formula to calculate the area and simple procedure to solve the irregular quadrilateral questions.

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Diagonal (e)
Diagonal (f)
Angle α

### Area of an Irregular Quadrilateral Formula

We are giving some important formulas that helps you to solve the area of an irregular quadrilateral. By having knowledge on the below mentioned formulas, you can easily solve any type of question effortlessly.

1. If diagonals of quadrilateral and angle between them is given,

Area = e * f * sin(α)

Where,

e, f are the lengths of 2 diagonals of a irregular quadrilateral.

α is the angle between angles.

2. If four sides and two opposite angles are given, then

Area = √[(s - a) * (s - b) * (s - c) * (s - d) - a * b * c * d * cos^2(θ/2)]

Where,

a, b, c, d are the sides of a quadrilateral

s = (a + b + c + d) / 2, θ = θ1 + θ2

3. If bimedians and angle between them is given,

Area = m * n * sin(θ)

Where,

m, n are bimedians

θ is the angle between bimedians

### How to Find Area of an Irregular Quadrilateral?

Irregular quadrilateral is a quadrilateral where all the sides and angles are not having equal length. Go through the following steps and get the instructions to calculate the irregular quadrilateral area. Make use of of any of these processes and get the answer.

Process 1:

• At first, divide the quadrilateral into two triangles by drawing diagonal that does not disturb the known interior angle.
• Calculate the area of each triangle by using the formula 1/2 * (base) * (height)
• Add areas of those two triangles to obtain the quadrilateral area.

Process 2:

• From the given question, observe the lengths of two diagonals and angle between them.
• Find the sine function of angle.
• Multiply the lengths of diagonals and multiply the product with sin(angle).
• Obtained value is called area of the irregular quadrilateral.

### Solved Examples on Irregular Quadrilateral Area

Example 1: In a quadrilateral the diagonal is 42 cm and the two perpendiculars on it from the other vertices are 8 cm and 9 cm respectively. Find the area of the quadrilateral?

Solution:

Given that

AC = 42 cm

BN = 9 cm

DM = 8 cm

Area of ABCD = area of Δ ABC + area of Δ ACD

= ½ * 9 * 42 + ½ * 8 * 42

= 9 * 21 + 4 * 42

= 189 + 168 = 357

∴ Area of Quadrilateral is 357 cm²

Example 2: Find area of irregular quadrilateral? If the length of diagonals is 10 cm, 15 cm with an angle 60 degrees.

Solution:

Given that,

Diagonal length e = 10 cm, f = 15 cm

Angle α = 60 degrees

Area = e * f * sin(α)

Put the values in the formula.

A = 10 * 15 * sin(60)

= 150 * (√3 / 2)

= 129.90

∴ Area of Quadrilateral is 129.90 cm²

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### FAQS on Area of an Irregular Quadrilateral Calculator

1. What is the difference between a regular and an irregular quadrilateral?

Quadrilaterals are of two types, regular and irregular. Regular quadrilateral is a quadrilateral when all the sides are in equal length. Irregular quadrilateral is exactly opposite to the regular one. The examples of regular quadrilateral is square, pentagon, etc. Irregular quadrilateral examples are rectangle, kite, parallelogram.

2. How do you define the area of an irregular quadrilateral?

An irregular quadrilateral is a closed figure having four sides and four angle. The length of all the sides and angle are not same. You must know either the length of all sides or diagonals and angle between the diagonals to find the area of an irregular quadrilateral.

3. What is an example of an irregular quadrilateral?

The some of real time irregular quadrilaterals are trapezoid, rectangle, kite, rhombus, and parallelogram.