# Area Of Quadrant

A circle is defined as the locus of all the points that are equidistant from the center. Now, a quadrant is one-fourth section of a circle which is obtained when a circle is divided evenly into four sections or rather 4 quadrants by a set of two lines which are perpendicular in nature. In this article, let us discuss what a quadrant is, how to calculate the area of the quadrant with examples in detail.

## What is Quadrant?

Quadrant refers to the four quarters in the coordinate plane system. Each of the four sections is called a quadrant. When it comes to circle, the quarter of a circle is called a quadrant, which is a sector of 90 degrees. When four such quadrants are joined, the structure that we get is nothing but a circle.

Fig 1. A circle with a quadrant ABO

In the above figure (Fig 1.), we can see a circle with one of the quadrants ABO coloured in green colour and angle AOB makes a right angle (90^{o}) at the centre O.

## How to Calculate the Area of a Quadrant?

To calculate the area of a quadrant of a circle, we must know the area of a circle.

To find the area of circle C, we need to know the following terms.

- Center: a point O of a circle from where all other points are equidistant.

- Radius: is defined as length of a line segment R from the centre point O

to anywhere on the perimeter of the circle.

- Diameter: is defined as a line segment D twice as the length of the

radius R. That is, D=2R

- The circumference is defined as the distance around the edge of a circle C.

(i.e.,) circumference/perimeter of a circle = 2πr, where π= 3.14159.

- The area is defined as the number of square units contained inside the circle,

that is, pi (π) multiplied by the radius squared (r^{2}).

Therefore, the area of a circle, A=πr^{2}

Now, to calculate the area of a quadrant, divide the area of a circle by 4 (as four quadrants make a circle). We get,

**Area of a quadrant, A= (πr ^{2})/4 Square units.**

### Area of a Quadrant Example

Let us see an example.

**Example:**

Find the area of a quadrant Q of a circle C with radius 8 cm.

**Solution: **

Given,

Radius, r = 8 cm

Area of circle= πr^{2}

= 3.14(8)^{2}

= 200.96 cm^{2}

Now, to calculate the area of a quadrant Q of circle C, divide the area of the circle by 4.

Area of quadrant, A1 = area of circle / 4

= 200.96/ 4

= 50.24 cm^{2}