Area Formula For Quadrilaterals

Area Formula for Quadrilaterals

Quadrilateral area formulae are used to compute the area of a closed figure with four sides, known as a quadrilateral. There are several varieties of quadrilaterals based on the qualities of distinct factors. In the next sections, we will learn how to calculate quadratic areas.

What are Quadrilateral Area Formulas?

Different quadrilateral area formulae are used for various quadrilateral types. Quadrilaterals include squares, rectangles, parallelograms, rhombuses, kites, trapezoids, and many more. Here are the formulae for the parallelogram, square, trapezium, rectangle, and kite areas.

The area of a quadrilateral is the measure of the region contained by its four sides, and it is measured in square units such as metres, inches, and centimetres. The method for calculating the area of a quadrilateral is determined by its kind and the information available about it. Quadrilaterals are closed two-dimensional shapes that have four sides, four edges, and four corners.

There are two kinds of quadrilaterals:

1. Regular quadrilateral: A quadrilateral with sides that are equal in length.

2. Irregular quadrilateral: A quadrilateral with sides that are not all equal.

Area Formulas of Quadrilaterals

The table below contains formulas for calculating the area of quadrilaterals of various types.

Name of Quadrilateral Area of Quadrilateral Formulas
Square Area of a square formula = (side)2
Rhombus Area of a rhombus formula = (1 ⁄ 2) × product of diagonals
Kite Area of a kite formula = (1 ⁄ 2) × product of diagonals
Parallelogram Area of a parallelogram formula = base × height
Rectangle Area of a rectangle formula = length × breadth
Trapezoid Area of a trapezoid formula = 1/2 × (sum of the lengths of parallel sides) × height

Area of Quadrilateral Using Heron’s Formula

We know that Heron’s formula is used to find the area of a triangle if three sides of the triangle are given. Follow the given procedure to find the area of the quadrilateral.

Step 1: Divide the quadrilateral into two triangles using a diagonal whose diagonal length is known.

Step 2: Now, apply Heron’s formula for each triangle to find the area of a quadrilateral.

[If a, b, c are the sides of a triangle, then Heron’s formula to find the area of a triangle is

Area of triangle = √[s(s-a)(s-b)(s-c)] square units

Where “s” is the semi-perimeter of triangle, which is equal to (a+b+c)/2. ]

Step 3: Now add the area of two triangles to get the area of a quadrilateral.

Solved Example For Quadrilateral Formula for Area

Example 1:  Determine the area of a cyclic quadrilateral with sides measuring 21, 35, 62, and 12 meters.

Solution: a = 12 m, b = 36 m, c= 62 m, d = 30 m


s = (21+35+62+12)/2

s = 140/2

s = 70 m

$$A = \sqrt{\left ( s-a \right )\left ( s-b \right )\left ( s-c \right )\left ( s-d \right )}$$

$$A= \sqrt{\left ( 70-12 \right )\left ( 70-36 \right )\left ( 70-62 \right )\left ( 70-30\right )}$$

$$A = \sqrt{58\times 34\times 8\times 40}$$

$$A =\sqrt{631040}$$

$$A = 794.38m^{2}$$

Maths Related Formulas
Compound Interest Formula Sum Of Squares Formula
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Simple Interest Formula Exponential Distribution Formula
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The Distance Formula Linear Interpolation Formula
Standard Deviation Formula Monthly Compound Interest Formula
Area Of A Circle Formula Probability Distribution Formula
Area Of A Rectangle Formula Proportion Formula
Area Of A Square Formula Volume Of A Triangular Prism Formula

FAQs (Frequently Asked Questions)

1. Is square a quadrilateral?

Yes, Square has four equal sides and angles, making it a quadrilateral.

2. How to calculate the area of a quadrilateral?

The quadrilateral is the combination of the basic geometric shape called triangles. To calculate the area of a quadrilateral, the area of the individual triangles should be computed, and add the area of the individual triangles.

3. What is the area of a quadrilateral?

The area of the quadrilateral is the space occupied by the shape quadrilateral in the two-dimensional space. As we know, a quadrilateral is a 2D figure with four sides. Generally, a quadrilateral is the combined form of a regular or an irregular triangle.