Question

Find the area of the shaded region. Leave your answer in terms of pi.

A. (243pi+162) ft^2
B. (243pi-162) ft^2
C. (27pi+162) ft^2
D. (27pi-162) ft^2

Answer 1

ANSWER

A. (243pi+162) ft^2

EXPLANATION

The area of the shaded region is the sum of the area of the major sector and the area of the isosceles triangle.

Area of major sector

$= \frac{360 - 90}{360} \times \pi \times {18}^{2}$

$= 243\pi {ft}^{2}$

The area of the isosceles triangle is calculated using the formula;

$= \frac{1}{2} {r}^{2} \sin( \theta)$

$= \frac{1}{2} \times {18}^{2} \sin(90 \degree)$

$= 162 {ft}^{2}$

The area of the shaded region

$= (243\pi + 162) {ft}^{2}$

The correct answer is A.