SOLUTION: Find the area of the shaded regions. Express the answer as a single fraction in simplest terms. https://imgur.com/a/gROF8I8

Algebra ->  Surface-area -> SOLUTION: Find the area of the shaded regions. Express the answer as a single fraction in simplest terms. https://imgur.com/a/gROF8I8      Log On


   

Question 1206922: Find the area of the shaded regions. Express the answer as a single fraction in simplest terms. https://imgur.com/a/gROF8I8
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Focus entirely on the semicircle up top.

A full circle has area of pi*r^2
r = radius

Half of which is 0.5*pi*r^2 and this is the area of a semicircle
area = 0.5*pi*r^2
area = 0.5*pi*12^2
area = 72pi

Then find the area of the right triangle that resides inside the upper semicircle.
area = 0.5*base*height
area = 0.5*(2*12)*9
area = 108

Subtract the two results to get the answer.
shadedArea = semicircleArea - triangleArea
shadedArea = 72pi - 108
The units for the area are "square centimeters".

To get an approximate version of the answer, replace pi with something like 3.14