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

Aug 25, 2016

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.

$A = \frac{1}{2} \times \pi \times {8}^{2}$

$A = \frac{1}{2} \times \pi \times 64$

A = 32pi " cm^2

We can confirm this using the formula for area of a semi-circle, $A = \frac{{r}^{2} \pi}{2}$.

$A = \frac{{8}^{2} \pi}{2}$

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!