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# Area of Circle – Explanation & Examples

To recall, the area is the region that occupied the shape in a two-dimensional plane. In this article, you will learn the area of a circle and the formulas for calculating the area of a circle.

## What is the Area of a Circle?

**The area of the circle is the measure of the space or region enclosed inside the circle. In simple words, the area of a circle is the total number of square units inside that circle.**

**For example**, if you draw squares of dimensions 1cm by 1cm inside a circle. Then, the total number of full squares located inside the circle represents the area of the circle. We can measure the area of a circle in m^{2}, km^{2}, in^{2}, mm^{2, }etc.

## Formula for the Area of a Circle

The area of a circle can be calculated using** three formulas**. These formulas are applied depending on the information you are given.

Let us discuss these formulas for finding the area of a circle.

### Area of a circle using the radius

Given the radius of a circle, the formula for calculating the area of a circle states that:

**Area of a Circle = πr ^{2} square units**

A = **πr ^{2} square units**

Where A = the area of a circle.

pi (π) = 22/7 or 3.14 and r = the radius of a circle.

Let’s get a better understanding of this formula by working out a few example problems.

*Example 1*

Find the area of a circle whose radius is 15 mm.

__Solution__

A = πr^{2} square units

By substitution,

A = 3.14 x 15^{2}

= (3.14 x 15 x 15) mm^{2}

= 706.5 mm^{2}

So, the area of the circle is 706.5 mm^{2}

*Example 2*

Calculate the area of the circle shown below.

__Solution__

A = πr^{2} square units

= (3.14 x 28^{2}) cm^{2}

= (3.14 x 28 x 28) cm^{2}

= 2461.76 cm^{2}

*Example 3*

The area of a circle is 254.34 square yards. What is the radius of the circle?

__Solution__

A = πr^{2} square units

254.34 = 3.14 x r^{2}

Divide both sides by 3.14.

r^{2 }= 254.34/3.14 = 81

Find the square root of both sides.

√r^{2} = √81

r = -9, 9

Since the radius cannot have a negative value, we take positive 9 as the correct answer.

So, the radius of the circle is 9 yards.

*Example 4*

Lawn sprinkler sprays water 10 feet in every direction as it rotates. What is the area of the sprinkled lawn?

__Solution__

Here, the radius is 10 feet.

A = πr^{2} square units

= 3.14 x 10^{2}

= (3.14 x 10 x 10) sq. ft

= 314 sq. ft

Therefore, the area of the sprinkled lawn is 314 sq. ft.

### Area of a circle using the diameter

When the diameter of a circle is known, the area of the circle is given by,

**Area of a Circle = πd ^{2}/4 square units**

Where d = the diameter of a circle.

*Example 5*

Find the area of a circle with a diameter of 6 inches.

__Solution__

A = πd^{2}/4 square units

= 3.14 x 6^{2}/4 Sq. inches.

= (3.14 x 6 x 6)/4 Sq. inches

= 28.26 sq. inches

So, the area of the circle with a diameter of 6 inches is 28.26 square inches.

*Example 6*

Calculate the area of the circle shown below.

__Solution__

Given the diameter,

A = πd^{2}/4 square units

= 3.14 x 50^{2}/4

= (3.14 x 50 x 50)/4

=1962.5 cm^{2}

*Example 7*

Calculate the area of a dinner plate, which has a diameter of 10 cm.

__Solution__

A = πd^{2}/4 square units

= 3.14 x 10^{2}/4

= (3.14 x 10 x 10)/4

= 78.5 cm^{2}

*Example 8*

The diameter of a circular plate is 20 cm. Find the dimensions of a square plate that will have the same area as the circular plate.

__Solution__

Equate the area of the circle to the area of the square

πd^{2}/4 = s^{2}

3.14 x 20^{2}/4 = s^{2}

s^{2 }=314

Find the square root of both sides to get,

s = 17.72

Therefore, the dimensions of the square plate will be 17.72 cm by 17.72 cm.

*Example 9*

Find the diameter of a circle with an area of 156 m^{2}.

__Solution__

A = πd^{2}/4

156 = 3.14d^{2}/4

Multiply both sides by 4.

624 = 3.14d^{2}

Divide both sides by 3.14.

198.726 = d^{2}

d = 14.1 m

Thus, the diameter of the circle will be 14.1 m.

### Area of a circle using the circumference

As we already know, the circumference of a circle is the distance around a circle. It is possible to calculate the area of a circle given its circumference.

**Area of a circle = C ^{2}/4π**

**A = C ^{2}/4π**

Where C = the circumference of a circle.

*Example 10*

Find the area of a circle whose circumference is 25.12 cm.

__Solution__

Given the circumference,

Area = C^{2}/4π

A = 25.12^{2}/4π

= 50.24 cm^{2}

*Example 11*

What is the circumference of a circle whose area is 78.5 mm^{2}?

__Solution__

A = C^{2}/4π

78.5 = C^{2}/4π

Multiply both sides by 4π.

C^{2} = 985.96

Find the square root of both sides.

C = 31.4 mm.

So, the circumference of the circle is 31.4 mm.