Area of a circle is the total surface bounded by the circumference of the circle. A circle is any two dimensional geometric figure which consist of all set of those points in a plane that are equidistant from a fixed point called center. On this page we will discuss the area of a circle in detail.

How to find the area of a circle.

There are formulas we use to find the area of a circle. We can find the area of a circle when given the radius and also when given the diameter of the circle.

Formulas for finding the area of a circle.

• The area of a circle = πr², where the π is constant (i.e π = 22/7 or 3.142) and r is the radius of the circle.

• Also, the area of a circle = 1/4 πd², where π is constant (i.e π=22/7 or 3.142) and d = diameter of the circle. Note that diameter two the radius (i.e d = 2r). Also note the following formulas very carefully. Whenever the pi (π) is not given, we take π = 22/7 or 3.142.

Lets understand better how to substitute these formulas by working some examples of the area of a circle.

Example 1. Find the area of a circle whose radius is 7cm. (Take π = 22/7).

Solution

In this question, since the radius of the circle is given, we find the area of the circle using the formula that contains radius. i.e

The area of a circle = πr², where π=22/7 and r = 7cm.

= 22/7 × 7²

= 22 × 7, (since 22/7 × 7×7 = 22 × 7)

= 154cm²

∴ The area of a circle = 154cm²

Example 2. Find the area of a circle whose diameter is 14cm.

solution

The area of a circle = 1/4πd², where π= 22/7 and the d=14cm.

= 1/4 × 22/7 × 14²

= 1/4 × 22 × 7 × 14

= 1/4 × 154 × 14

= 38.5×14

= 539cm²

∴ The area of a circle is = 539cm²