Area of a quarter circle is one-fourth part of the whole area of the circle. When a circle is divided into four equal parts, each part is called the quarter of a circle. Each quarter is called the quadrant of the circle. So, the area of a quarter circle is times of area of the circle.

## What is the area of a quarter circle?

A circle is a geometric figure that traces the path of all those points, which is equidistant to a unique point called the centre of the circle. A quarter of a circle is one-fourth part of the whole circle. Therefore, the area of a quarter circle is the fourth part of the whole area of a circle.

The formula for the area of a quarter circle using radius

If a circle has a length of radius r, then the area of the circle, A = r2

Then, the area of a quarter circle = times of A

= ¼ × πr2 = πr2/4

The formula for the area of a quarter circle using the diameter

If the length of the radius is r, then the length of the circle’s diameter, d = 2r, that is, r = d/2.

Then, the area of circle = π(d/2)2 = πd2/4

Area of a quarter circle = ¼ × π(d/2)2 = πd2/16

### Area of a quarter circle related articles

- Circumference of a circle
- Circle and its parts
- Area of a circle
- Quadrants

## Solved examples on the area of a quarter circle

Example:

A circle has a radius of 14 cm, find the area of a quarter circle.

Solution:

Radius of circle = 14 cm

Area of a quarter circle = πr2/4 = 22/7 × ¼ × 14 × 14 = 154 cm2

Example:

A circle has a diameter of 32 cm, find the area of a quarter circle.

Solution:

Diameter of circle = 32 cm

Area of a quarter circle = πd2/16 = 22/7 × 1/16 × 322 = 201.14 cm2

Example:

A goat is tied to one corner of a square field. The length of the rope to which the goat is tied is 2m. Find how much area is available for the goat to graze.

Solution:

The grazing field will be a quarter of a circle of radius 2 m.

Area of grazing field = Area of a quarter circle with radius 2 m

= πr2/4 = 22/7 × ¼ × 22 = 22/7 ≈ 3.14 m2

## Video Lessons on Circles

### Introduction to Circles

### Parts of a Circle

### Area of a Circle

### All about Circles

## Frequently Asked Questions (FAQs)

### What is the radius of a quarter of a circle?

The radius of a quarter of a circle is the same as the radius of the given circle.

### What is the area of a quadrant?

The area of a quadrant is the same as the area of a quarter circle which is πr2/4.

How to find the area of a quarter circle when the circumference of the circle is given?

With the value of the circumference of the circle, find the radius of a circle. Then substitute the value of the radius of the circle in the formula of area of a quarter circle using radius which is πr2/4.

### What will be the area of four quarter circles?

Together four quarter circles make a whole circle. Therefore, the area of four quarter circles is equal to the area of the circle.