Question

Find the area of the shaded portion in the circle.

Answer 1

is 12 a radius or diameter

Answer 2

I believe it is the diameter

Answer 3

area of bottom half of shaded area is

1/2 * 6^2 Pi

18 Pi

Since it is half of whole circle

Answer 4

Shaded area is the sum of 1/2 the area of the circle plus the area of the segment:\[\left(\frac{1}{2}\pi r^2\right)+\left(\frac{1}{2} r^2(\theta -\text{Sin}[\theta ])\right) \]where theta is the angle of the sector. Substitute the following values into the above expression:\[r=6\text{, }\theta =\pi -2\text{ArcTan}\left[\frac{3}{12}\right] \]The result is, \[18 \pi +18 \left(\pi -2 \text{ArcTan}\left[\frac{1}{4}\right]-\text{Sin}\left[2 \text{ArcTan}\left[\frac{1}{4}\right]\right]\right)= 95.8075 \]

Answer 5

please see the file i have attached
hope it helps

Answer 6

@ shanna, I am reviewing the result and it may take awhile. It's 13:14 California time now.

Answer 7

@ shanna

A revised solution is attached as a Mathematica pdf file. Thank you for coming forward with your solution.