Question

A

,
B
and
C
are points on a circle with
A
C
as a diameter.
A
B
C
is a right-angled triangle.

Work out the total area of the regions shaded in the diagram.
Give your answer correct to 1 decimal place.

Answer 1

Area of the shaded portion = 54.5 cm²

Explanation:

Solve first for the area of the circle:

`area \: of \: circle = \pi {r}^(2) \\ = \pi( (d)/(2) )^(2) \\ = \pi( (10)/(2) )^(2) \\ = 25\pi \: or \: 78.5398 {cm}^(2)`

Then, compute for the area of the triangle:

`area \: of \: triangle = (1)/(2) * base * height \\ = (1)/(2) ( {8})(6) \\ = 24 {cm}^(2)`

Since we only needed the shaded portion, we have to subtract the area of the triangle from the area of the circle

`25\pi {cm}^(2) - 24 {cm}^(2) = 54.5398 {cm}^(2)`