Answer:
Perimeter of the shaded region is 268 m
Step-by-step explanation:
In this diagram a semi circle is drawn inside a rectangle of length 150m.
Length of diameter of a semicircle = 150 m
So radius of the semicircle = ![\frac{150}{2}=75 m](https://tex.z-dn.net/?f=%5Cfrac%7B150%7D%7B2%7D%3D75%20m)
We have to find the perimeter of the shaded region.
Perimeter of the shaded region = length of tangents drawn on the circle at A and B + m(arc AB)
Length of tangents = radius of the semi circle = 75 m
and m(arc AB) = ![\frac{\text{Perimeter of the circle}}{4}=\frac{2\pi r}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BPerimeter%20of%20the%20circle%7D%7D%7B4%7D%3D%5Cfrac%7B2%5Cpi%20r%7D%7B4%7D)
= ![\frac{2\pi (75)}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B2%5Cpi%20%2875%29%7D%7B4%7D)
=
\
= ![\frac{471}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B471%7D%7B4%7D)
= 117.75 m
Now Perimeter of the shaded region = 75 + 75 + 117.75
P = 267.75 ≈ 268 m