Question

acellusFind the area of the shaded region.6005 cmA = [?] cm2Enter a decimal rounded to the nearest tenth.

Answer 1

Answer:

76.3

Explanation:

The area of a segment is given by the formula

$segment\; area=(\frac{\pi\theta}{360}-\frac{\sin\theta}{2})\times r^2$

The segment is the red region.

Therefore, the area of the shaded region given in the picture of the question is

Area of the circle - Area of the segment.

Since

$Circle\; Area=\pi r^2$

and

$segment\; area=(\frac{\pi\theta}{360}-\frac{\sin\theta}{2})\times r^2$

The area of the shaded region is

$Area\; Shaded=\pi r^2-(\frac{\pi\theta}{360}-\frac{\sin\theta}{2})\times r^2$

Now, in our case,

$\begin{gathered} \theta=60^o \\ r=5 \end{gathered}$

Therefore,

$Area\; Shaded=\pi\cdot5^2-(\frac{\pi(60)}{360}-\frac{\sin60}{2})\times5^2$

Evalauting the right-hand side gives

$Area\; Shaded=76.27516$

Rounded to the nearest tenth, the above is

$\boxed{Area\; Shaded=76.3}$

which is our answer!