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=(a+b+c+d)/2
s = (21+35+62+12)/2
s = 140/2
s = 70 m
| $$A = \sqrt{\left ( s-a \right )\left ( s-b \right )\left ( s-c \right )\left ( s-d \right )}$$ |
$$A= \sqrt{\left ( 70-12 \right )\left ( 70-36 \right )\left ( 70-62 \right )\left ( 70-30\right )}$$
$$A = \sqrt{58\times 34\times 8\times 40}$$
$$A =\sqrt{631040}$$
$$A = 794.38m^{2}$$