Easy Ways to Calculate the Area of Squares and Circles

By Robert O

Circles and squares are basic shapes that we interact with within our everyday lives. Most of the objects have these shapes. The knowledge of their areas and perimeters is key in making such objects. Think of your ventilation holes on the wall as an example. What of those circular windows?

In this tutorial, we will shift our focus to squares and circles. You check on other shapes from our previous tutorials.

How to compute an area of a circle?

A circle has a diameter and radius that defines its area. The diameter stretches from one end of the circle to the other end and passes through the center. The radius is half of this distance.

We calculate the area of a circle, A, by:

    \[A=\pi r^{2}\]

Where π (pie) is a constant equal to

    \[\frac{22}{7}\]

If you have a semi-circle (half a circle), then the formula becomes:

    \[A=\frac{1}{2} \pi r^{2}\]

Similarly, for a quarter circle, the area is

    \[A=\frac{1}{4} \pi r^{2}\]

Note: If you have the diameter, ensure to divide it by two to get the radius before substituting the values into the formula.

Example 1

The diameter of a center circle of a football pitch is 14 feet. What is the area?

Solution

Find the radius by dividing the diameter by two.

    \[r=\frac{d}{2}=\frac{14}{2}=7 \text { feet }\]

    \[A=\pi r^{2}\]

    \[A=\frac{22}{7} \times 7^{2}=154 \mathrm{sq} \cdot \mathrm{ft}\]

Example 2

A swimming pool has two semicircular ends of a radius of 10m each. What is the total area of the two semicircular ends?

Solution

If we combine the two semicircles, we get a full circle of radius 10m. Therefore, the total area is:

    \[A=\pi r^{2}\]

    \[A=\frac{22}{7} \times 10^{2}=314.29 \mathrm{~m}^{2}\]

How to compute the area of a square?

A square is a four-sided figure where all sides have equal dimensions. It is a figure whose area is simple to calculate since you simply square one side.

The area of the above square is:

    \[A=L \times L=L^{2}\]

Example 3

A square room measuring 12 feet on all sides is to be fully covered with a carpet. Find the area of the carpet needed.

Solution

A square room needs a square carpet.

Area of the carpet, A, is:

    \[A=L \times L=L^{2}\]

    \[A=12^{2}=144 \text { sq. feet }\]

Example 4

A carpenter wants to design a dining table with a square top measuring 6 feet on all sides using a block of composite wood. What is the surface area of the composite wood needed?

Solution

    \[A=6^{2}=36 \text { sq. } \mathrm{feet}\]

Remarks

Squares and circles are all regular shapes whose areas are easy to calculate using formulas. You only need to recognize that the shape is either a circle or a square and then apply an appropriate formula.

About the Author

This lesson was prepared by Robert O. He holds a Bachelor of Engineering (B.Eng.) degree in Electrical and electronics engineering. He is a career teacher and headed the department of languages and assumed various leadership roles. He writes for Full Potential Learning Academy.