Question

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

Answer 1

76.3

Explanation:

The area of a segment is given by the formula

`segment\; area=((\pi\theta)/(360)-(\sin\theta)/(2))* 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=((\pi\theta)/(360)-(\sin\theta)/(2))* r^2`

The area of the shaded region is

`Area\; Shaded=\pi r^2-((\pi\theta)/(360)-(\sin\theta)/(2))* r^2`

Now, in our case,

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

Therefore,

`Area\; Shaded=\pi\cdot5^2-((\pi(60))/(360)-(\sin60)/(2))*5^2`

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!