The question is find the area of the shaded segment. I just need a brief explanation with the answer

Question

asked May 20, 2023 45.7k views

1 Answer

Joel Wembo · Answer 1 · 2023-05-25T23:55:53+0000

SOLUTION

The formula for area of segment is given to be

$A=(\theta)/(360)\pi r^2-(1)/(2)r^2\sin \theta$

From the image

$\theta=120^(\circ),r=4$

substituting these values gives

$A=(120)/(360)*\pi(4)^2-(1)/(2)(4)^2\sin 120$

Solve for A

$\begin{gathered} A=(1)/(3)*\pi*16^{}-(1)/(2)*16*^{}0.8660 \\ A=16.76-6.93 \\ A=9.83 \end{gathered}$

Therefore, the area of the shaded segment is 9.83 square meters