Question 1166971: In the diagram, O is the centre of the circle and sector angle COB is 120 degrees. CB has arc length 4 π cm. Also AC=AB. Find the area, in cm*2, of the shaded region.
A)30
B)18 √ 3
C) 27 √ 3
D) 27
E) 24 √ 3
https://imageshack.com/i/pn2akcrPj
Found 2 solutions by Boreal, ankor@dixie-net.com:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! It is B. We know the radius is 6 cm because the 120 degree arc is 4π so the perimeter is 12π. C=2πr
the shaded area may be divided in half by drawing the radius through the center. This gives rise to two larger triangles. The angle at the vertex was originally 60 degrees, because the arc is 120 degrees. That makes the new triangles 30-30-150 and the two right triangles made from it are 30-60-90 with the altitude being 3, because the hypotenuse is the radius.
If the altitude is 3, the adjacent side is 3 sqrt (3)
The area of one of those triangles is (1/2)bh, so the area of all 4 of them, 2 on bottom and two on top, is 2(3*3sqrt(3), and that is 18 sqrt (3)
Answer by ankor@dixie-net.com(22740)  (Show Source):
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