# Area of a Circle

The area of a circle can be found using the formula for the area of a circle shown below in blue.

A = π × r2

A = area

π = 3.14

If r is known, you simply need to substitute the known value for r in the formula.

Example #1:

Calculate A if r = 4 inches

A = pi × r2 = 3.14 × 42 = 3.14 ×16 = 50.24 inches2

Notice that the unit (inches) is squared to show that it was multiplied by itself twice.

Example #2:

Calculate A if r = 6 inches

A = pi × r2 = 3.14 × 62 = 3.14 × 36 = 103.04 inches2

## Interesting examples showing how to find the area of a circle and the radius if the area is given

Examples #3

If D = 20 cm, calculate the area of this circle.

There is a couple of ways to solve this.

The first way is to get r and then replace its value.

Since r is half the diameter, r = 20 divided by 2

r = 10 cm

A = pi × r2 = 3.14 × 102 = 3.14 × 100 = 314 cm2

The other way to solve this is to use the diameter.

We will need to express the formula in terms of the diameter.

The radius is half the diameter

r  =
d / 2

Replace r into the formula A = πr2.

Notice that r2 = r × r

 r × r =   d / 2 ×   d / 2
Notice that r2 = r × r

 r × r =   d / 2 ×   d / 2

r × r =
d × d / 2 × 2

r × r =
d2 / 4

A  =  π ×
d2 / 4

Let's us use the formula above now to see if we get the same answer.

A  =  3.14 ×
202 / 4

A  =  3.14 ×
400 / 4

A  =  3.14 × 100

A = 314 cm2

Examples #4

If A = 78.5 inches2, find r or the radius of the circle

Review solving multiplication equations before looking at the solution below. r = 5 inches because 52 = 5 × 5 = 25

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