Question

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

Answer 1

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