Question

What is the area of a semicircle with radius `8` cm?

Answer 1

Consider a circle of radius `8` centimetres. Recall that the centre angle in a circle is always `360˚`. However, a semi-circle is a circle cut in half. Hence, the centre angle for the semi-circle is cut in half, or has a measure of `180˚`.

Here's a diagram of what's going on.

Before applying the formula, let's convert `180˚` to radians.

`(180˚)/1 xx pi/(180˚) = pi`

We will now use the formula to determine the area of this semi-circle.

`A = 1/2 xx pi xx 8^2`

`A = 1/2 xx pi xx 64`

`A = 32pi " cm^2`

We can confirm this using the formula for area of a semi-circle, `A = (r^2pi)/2`.

`A = (8^2pi)/2`

`A = 32 pi" cm^2`

Same, so both formulae work.

Here are a few problems for you practice.

Practice exercises:

Determine the area of the following semi-circles.

a) The semi-circle contained inside a circle of radius `5` inches.

b) The semi-circle contained inside a circle of diameter `22` feet.

c) The semi-circle contained inside a circle of circumference `18` meters.

Hopefully this helps, and good luck!