Question 1197946
<font color=black size=3>
It depends on where the shaded region is located. Is it to the left of the mirror line? Or to the right? Unfortunately you haven't specified.


But luckily there are answer choices to pick from which will help narrow down the correct region.


This is probably what the diagram looks like
<img src = "https://i.imgur.com/RlkbKVm.png">
I'm placing point A as the center, rather than C. But feel free to swap those letters if you prefer.
The colored regions aren't necessarily what is shaded in the diagram of your textbook. 
They're shaded that way to break the figure into manageable pieces.


d = 24 = diameter
r = d/2 = 24/2 = 12 = radius
The radius goes from A to B, and also from A to D.
This explains how AB = 12 and AD = 12.


The dashed vertical mirror line will have point D reflect over it to land on point A, which is the center of the circle.
Because of this mirror symmetry, we know that AE = ED
Furthermore, AE = AD/2 = 12/2 = 6


Focus on triangle AEB. 
This is a 30-60-90 triangle because of the fact hypotenuse AB = 12 is exactly double that of the short leg AE = 6. 
This makes the long leg BE = 6*sqrt(3).


Recall that 
longLeg = shortLeg*sqrt(3)
which applies to 30-60-90 triangles exclusively.


Since we know we're dealing with a 30-60-90 triangle, we know that angle EAB is 60 degrees. 
This doubles to 2*60 = 120 degrees to represent angle BAC.
This doubling process is valid because triangles EAB and EAC are congruent, which in turn makes angle EAB = angle EAC.


The portion of the circle not shaded red (including the blue region) is 120/360 = 1/3 of the circle. 
Therefore, the red shaded region is the remaining 2/3 of the circle.


The area of the full circle of radius r = 12 is:
A = pi*r^2
A = pi*12^2
A = pi*144
A = 144pi


The red shaded area, shaped like pacman, is 2/3 of that full area.
red shaded area = (2/3)*(144pi) = 96pi


-----------------------------------------------------


Now let's find the area of triangle EAB shaded in blue.
area = 0.5*base*height
area = 0.5*AE*BE
area = 0.5*6*6*sqrt(3)
area = 18*sqrt(3)


Double this result to get the area of triangle CAB.
2*18*sqrt(3) = 36*sqrt(3)
again this doubling process is valid because triangles EAB and EAC are congruent.


Then combine this with the 96pi found earlier to get the area of everything to the left of the dashed mirror line.


96pi+36*sqrt(3)


This is not listed as one of the answer choices, so we'll see if we can find the area of the region to the right of the mirror line.


We subtract from 144pi, which was the area of the full circle
144pi - (96pi+36*sqrt(3))
144pi - 96pi - 36*sqrt(3)
48pi - 36*sqrt(3)
This is listed as one of the answer choices. So this is likely the correct answer. 
Of course this is assuming the shaded region in your textbook is to the right of the mirror line.


-----------------------------------------------------



Answer: <font color=red>choice E) 48pi - 36*sqrt(3)</font>
</font>