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!