Question

A sector has radius 12 and central angle 64°. Find the area of the sector.

Answer 1

We need to find the area of the sector which is given by the next formula:

Area of the sector = ( central angle / total angle ) * area of the circle

First, we need to find the area of the circle:

$\begin{gathered} A_c=\pi\ast r^2 \\ Replacing \\ A_c=\left(12\right)^2\pi \\ A_c=144\pi \end{gathered}$

Now, we can use the formula for the area of the sector

Central angle = 64

The total angle of a circle= 360

Area of the circle = 144π

Replacing using the formula:

Area of the sector = (64/360) * 144π

Area of the sector = 128π/5

Area of the sector = 80.42477