Question

Referring to the figures, find the area of the shaded regionshown. Round the answer to the nearest hundredth.

Answer 1

Given:

$r=3in;unshadedregion=45^{\circ}$

$\begin{gathered} \text{Shaded region (}\theta)=360^{\circ}-45^{\circ} \\ \text{Shaded region (}\theta)=315^{\circ} \end{gathered}$

$\begin{gathered} \text{Area of the shaded region=}\frac{\theta}{360}\times\pi\times r^2 \\ \text{Area of the shaded region=}\frac{315}{360}\times\frac{22}{7}\times3\times3 \\ \text{Area of the shaded region}=\frac{62370}{2520} \\ \text{Area of the shaded region}=24.75in^2 \end{gathered}$