Area of a Circle Support Page

On this webpage you will find step-by-step instructions and examples to help your child learn to work out the area of a range of circles.

Want to test yourself to see how well you have understood this skill?.

• Try our NEW quick quiz at the bottom of this page.

• Area is a measure of the amount of space inside a shape.
• It is measured in squares, so it can be square inches (in²), square cm (cm²), square feet(ft²), etc.

The formula for the area of a circle is: \[ A = \pi r^2 \] where r is the radius of the circle.

Area of a Circle Example 1

Find the area of the circle below to 1 decimal place.

To find the area of the circle, we need to find the radius first.

The radius is half of the diameter, so it is half of 5 = 2.5 cm.

Next we need to square the radius: 2.5² = 2.5 x 2.5 = 6.25 cm.

Finally we need to multiply this amount by pi (π).

So this gives us the area of the circle:

\[ A = \pi r^2 = \pi \times 6.25 \; or \; 6.25 \pi \]

If we take pi = 3.14, this gives us an area of 3.14 x 6.25 = 19.6 square cm (or 19.6 cm²) to 1 decimal place.

Area of a Circle Example 2

Find the area of the circle below to the nearest inch.

To find the area of a circle, we need to find the radius first.

The radius of the circle is half of the diameter which is half of 7 = 3.5 inches.

Next we need to square the radius: 3.5² = 3.5 x 3.5 = 12.25 cm.

Finally we need to multiply this amount by pi (π).

So this gives us the area of the circle:

\[ A = \pi r^2 = \pi \times 12.25 \; or \; 12.25 \pi \]

If we take pi = 3.14, this gives us an area of 3.14 x 12.25 = 38.5 square inches or 38.5 in² to 1 decimal place.

Area of a Circle Example 3

Find the area of the circle below and give your answer to the nearest whole number.

To find the area of a circle, we need to square the radius and multiply this by pi (π)

The radius of the circle is 12 m, so the square of the radius is 12² = 12 x 12 = 144.

Finally we need to multiply this amount by pi (π).

So this gives us the area of the circle:

\[ A = \pi r^2 = \pi \times 144 \; or \; 144 \pi \]

This gives us an area of π x 144 = 452 square m or 452 m² to the nearest whole number.

Area of a Circle Example 4

Find the radius of the circle if the area of the circle is 36 π square inches.

In this case, we know the area of the circle but we need to find the radius.

The area of the circle is:

\[ A = \pi r^2 \]

We know that the area is 36 π square inches so this gives us:

\[ 36 \pi = \pi r^2 \]

If we divide both sides of the equation by π then it cancels out, giving us:

\[ r^2 = 36 \]

If we square root both sides of the equation we end up with:

\[ r = \sqrt {36} = 6 inches \]

This gives us an answer of 6 inches for the radius of the circle.

Area of a Circle Example 5

Find the area of the circle which touches the edges of the square shown in the diagram below, giving your answer in terms of pi.

You will notice that the sides of the square are exactly the same length as the horizontal diameter of the circle.

This means that the diameter of the circle is 32 mm.

We halve the diameter to find the radius:

\[ r = 32 \div 2 = 16 mm \]

We can now find the area of the circle:

\[ A = \pi r^2 = \pi \times 16^2 = 256 \pi \]

For this question we have been asked to leave the answer in terms of pi.

This gives us an answer of 256 π mm² for the area of the circle .

Our Area of a Circle Calculator will find the area of any circle, if you type in a radius or diameter.

It will take whole numbers, fractions or decimal values.

The best thing about it is that it shows the working out, step-by-step.

We have a selection of worksheets to help you practice finding the area of different circles.

As well as basic area of a circle worksheets, we also have a selection of more challenging word problems connected to finding the area of a circle.

We have a range of other area worksheets and support pages for a range of different 2d shapes.

Here is our selection of free printable perimeter worksheets for 3rd and up.

Using these sheets will help your child to find the perimeter of a range of shapes including rectangles, rectilinear shapes, circles, quadrilaterals and regular shapes.

This quick quiz tests your knowledge and skill at finding the area of a circle here.

The link below will open the quiz in a dedicated quiz page or you can preview a copy of the quiz underneath.

The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

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