Area of a semicircle. Finding the area of semi circles.

Area of a semicircle video

To find the area of a semicircle first you need to find the area of the whole circle and divide your answer by 2, as a semicircle takes up half the space of a circle.

To find the area of the circle use A=π×r².  (A stands for the area of the circle, π is Pi and r is the radius of the circle).

Let’s take a look at an example.

Example 1

Find the area of this semicircle.

Answer

First find the area of the whole circle. Make sure that you use the radius of the circle (the distance halfway across the circle), this is 4 cm as the diameter is 8 cm (the distance all the way across the centre of the circle).

A = π×r²

A= π×4²

A= 50.3... cm²

Now all you need to do is divide the answer by 2

50.3... ÷ 2 = 25.1 cm² (1 d.p)

Example 2

A semicircular shaped doormat has a radius of 7cm. Calculate the area of the doormat.

Answer

To begin with first find the area of the circle by using A = π×r².

A = π×r²

A= π×7²

A= 154.1... cm²

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Again, all you need to do now is to divide the area of the circle by 2.

Do this by 154.1 ÷ 2 = 77.1 cm² (1 d.p)

Extra Tips

If you don’t have a scientific calculator then use Pi as 3.14 on your pocket calculator.

As you do more examples you might just want to use the formula A = π×r²/2. This will means less lines of working out.

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