Question

1AcellusFind the area of the shaded region.Help Resources80°5 cmA = [?] cm2Enter a decimal rounded to the nearest tenth.Enter

Answer 1

The formula for finding the area of the unshaded segment is given as

$A=(\frac{\pi\theta}{360}-\frac{\sin \theta}{2})r^2$

Given the following parameters,

π = 3.14

θ = 80°

r = 5 cm

Substituting,

$\begin{gathered} A=(\frac{3.14\times80}{360}-\frac{\sin \text{ 80}}{2})\times5^2 \\ =(\frac{251.2}{360}-\frac{0.9848}{2})\times25 \\ =(0.6978-0.4924)\times25 \\ =0.2054\times25 \\ =5.135\approx5.1\operatorname{cm}^2 \end{gathered}$

To find the area of the shaded portion, we would subtract the area of the unshaded segment from the area of the circle.

Area of circle = πr²

$3.14\times5^2=78.5\operatorname{cm}^2$

Therefore,

The area of the shaded region = 78.5 - 5.1 = 73.4 cm²