How to calculate the Area of Circle?

Geometry is a discipline that includes the study of plane shapes or flat shapes. A plane shape is a two-dimensional shape that does not consist of thickness as a dimension. Some of the plane shapes are rectangle, square, rhombus, pentagon, etc. It also gives formulas to calculate its parameters with the reference to the dimensions of the given figure.

In the given article there is a brief discussion about the shape circle with its properties. The article also shows the methods of finding the area of a circle using radius. Some of the sample numerical problems are given with their solutions for quick reference.

What is a Circle?

A circle is a flat geometrical figure having no edges or vertices. It is a figure formed by the connection of an infinite number of points. A circle has an infinite number of sides and the internal angles of which measure to be 180 degrees. 

Hence, a circle is a two-dimensional flat shape that can be plotted on a plane surface, with zero edges and vertices. The interior angle of the figure equals 180 degrees.

Properties of a circle

• A chord passing connecting two points of the circle and passing through the centre is known as diameter. A diameter is considered to be the longest chord of the circle.
• The radius is a line segment connecting any point of the circle and the centre of the circle. And, the radius which is perpendicular to the chord bisects the chord.
• An inscribed angle formed by a diameter is a right angle.
• The radius and circumference of the circle are directly proportional.

Circle

Area of a Circle

A circle is a two-dimensional, closed figure, and the total surface occupied or enclosed by the figure is known as its area. The area of a circle can be determined by using the length of the radius, length of the diameter, or the circumference of the circle. The standard formula for the calculation of the area of a circle is given pi multiplied by the square of the radius.

Mathematically this formula can be written as,

Area of circle(A) = π × (radius)²

For example:

If the radius of the given circle is 7cm, then the area of the circle will be given by

Area of circle(A) = π × (radius)²

=>A = 22/7 × 7

=>A = 22cm²

Sample Problems

Problem 1. If the radius of a circle is 14cm. Find the area of the given circle.

Solution:

Given 

Radius of the circle is 14cm

We have,

Area of circle(A) = π × (radius)²

=>A = 22/7 × 14²

=>A = 22 × 2 × 14

=>A = 616cm²

Hence, the area of the given circle is 616cm²

Problem 2. If the radius of a circle is 12cm. Find the area of the given circle.

Solution:

Given

Radius of the circle is 12cm

We have,

Area of circle(A) = π × (radius)²

=>A = 22/7 × 12²

=>A = 452.57cm²

Hence, the area of the given circle is 452.57cm²

Problem 3. If the radius of a circle is 49cm. Find the area of the given circle.

Solution:

Given

Radius of the circle is 49cm

We have,

Area of circle(A) = π × (radius)²

=>A = 22/7 × 49²

=>A = 22 × 7 × 49

=>A = 7546cm²

Hence, the area of the given circle is 7546cm²

Problem 4. If the radius of a circle is 35cm. Find the area of the given circle.

Solution:

Given

Radius of the circle is 35cm

We have,

Area of circle(A) = π × (radius)²

=>A = 22/7 × 35²

=>A = 22 × 5 × 35

=>A = 3850cm²

Hence, the area of the given circle is 3850cm²

Problem.5. If the radius of a circle is 42cm. Find the area of the given circle.

Solution:

Given

Radius of the circle is 42cm

We have,

Area of circle(A) = π × (radius)²

=>A = 22/7 × 42²

=>A = 22 × 6 × 42

=>A = 5544cm²

Hence, the area of the given circle is 5544cm²