Find the area of the shaded segment of the circle. (Round your answer to the nearest hundredth). (7.4 Segment of a Circle)

Question

asked Feb 8, 2023 36.1k views

1 Answer

Mmar · Answer 1 · 2023-02-14T04:29:55+0000

Answer: 353.77

Explanation:

Let's start by considering the sector ACB.

The area of this sector is
$\pi \cdot 24^(2) \cdot (120)/(360)=192\pi$

Now, let's consider the area of triangle ACB. Its area is given by:

$(1)/(2) \cdot 24 \cdot 24 \cdot \sin 120^(\circ)=144√(3)$

So the area of the shaded segment is
$192\pi -144√(3) \approx 353.77$