# How to find the area of a quadrant, formula | examples

The area of a quadrant is the measure of the amount of surface enclosed by the quadrant. A quadrant is one-quarter of the area of a circle. When two radii of a circle are at a right angle to each other they formed an angle of 90°. The area occupied by these two radii is called the area of a quadrant. This page will discuss the area of a quadrant in detail.

## How to find the area of a quadrant

The area of an enclosed (quadrant) is measured by finding the number of times a standard unit area will fit exactly into it. Since the area of the quadrant is a quarter of the area of a circle, we take one-fourth of the area of a circle to find the area of a quadrant. i.e the formula for finding the area of a quadrant is = 1/4 × πr^{2}, where π = 22/7 and r = radius of the circle. Let’s understand the area of a quadrant by working through some examples.

Example 1. If the area of a circle is 180cm^{2}. Find the area of the quadrant of the circle. [Take π = 22/7]

Solution

The area of a quadrant = 1/4 ×πr^{2}, where π=22/7 and the area of the circle = 180cm^{2}

= 1/4 × 22/7 × 180cm^{2}

= 1/4 × 3.142 × 180cm^{2}

= 1/4 × 565.56

= 141.39cm^{2}

∴ The area of the quadrant = 141.39cm^{2}

Example 2. If the radius of a circle is 7cm. Find the area of a quadrant. [Take π = 22/7]

Solution

The area of a quadrant = 1/4 × πr^{2}, where π = 22/7, and r = 7cm.

= 1/4 × 22/7 × 7^{2}

= 1/4 × 22 × 7

= 154/4

= 38.5cm^{2}

∴ The area of a quadrant = 38.5cm^{2}