Area Of A Circle Formula

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A circle is a figure having one line called the circumference, and it is drawn in such a way that all straight lines being drawn from the center point to the circumference are of equal lengths. You have probably come across different geometry problems like calculating the area of a square, area of a rectangle, or area of a triangle. These may be pretty straightforward, but what about if you are given an assignment to find the area of a circle. Here things may be a little different, however, you can use the information provided to get your answer.

First, you will need to know the formula you use to find the area of a circle. In its simplest form, finding the area of a given circle requires that you know the radius. But sometimes, you may not be given the radius and what you have are other information. That means you can use the data you have been given to try finding the area. Let us look at the different ways of finding the area of  a given circle, but before that, let’s see how a circle looks like.

This is how a circle looks like:

Let us look at how we find the area of a circle. 

Use of Radius to Find Area

The radius of a circle is the length you get when you draw a line from the center to the edge of a circle. The line can be drawn to any direction provided that it originates from the center and touches the line representing the circumference or the edge of the circle, and you will find that all the lines will be of the same lengths regardless of the part of the edge it touches. The radius is half the length of the diameter of the circle. Usually, the diameter connects opposite sides of a given circle passing through the center.

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Let’s say that we a given the radius as 7 cm.

You will need to write down the formula for finding the area of a circle, which is:

Area =

Where  usually called Pi, is a mathematical constant that represents the ratio you get between the circumference of a circle and the diameter of the same circle. In decimal numbers, it Pi or is approximately 3.14.


Area = 3.14 x

Area = 3.14 x 72

Area = 3.14 x 49

Area = 153.86 cm2

Usually, the area is given in square units. So if you had a radius that is in centimeters, you will have the area of the circle in square centimeters. In the event that you are given the radius in feet, you will give your answer in square feet. So when providing the area, make sure you put it in the measurements it is given.

Given the Diameter, How to You Calculate the Area of the Circle

Sometimes, you will be given the diameter and not provided with the radius. In this case, you have to figure out how to get the area.  We said that diameter is drawn to connect two opposite sides of a given circle. So it would be correct to say that the diameter is two times the radius.

If for example, you are given the diameter as 18 cm, the radius will therefore be 18 cm divide by 2.

So the radius will be 9 cm.

You now use the original formula to find the area of that circle.

Area =

Area = 3.14 x

Area = 3.14 x 92

Area = 3.14 x 81

Area = 254.34 cm2

Given The circumference, How do Your Calculate the Area

When you are given the circumference of a circle, you can use a revised formula of the area. In this revised formula, it uses circumference directly and there is no need for using the radius in finding the area of the given circle.

The revised formula is

Area = C2 divided by 4  where C represents the circumference

Area = C2/4

May be you would want to know how we arrived at the formula Area = C2/4

We know that the circumference of a circle is calculated using the formula:

C = d, where d is the diameter

And we know that diameter is two times the radius

So C = 2r, where r is the radius

Therefore, r = C/

Since area of a circle is

We say that:

Area =

Area =  x (C/2

Area = (C/2

Area =C2/42)

Area = C2/4

If you are given the circumference as 36 cm, you can use the above formula to find the area.

Area = 362 / 4

Area = 92()

Area = 81()

Area = 81 x 3.14

Area = 245.34 cm2

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Area of a Circle – How to Find the Area of Circle When we Know the Radius Explained

How to find the Area of a Circle When we know the Diameter

How to find the Area of a Circle When we know the Circumference

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