SSAT Math Question 307: Answer and Explanation
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Question: 307
1. In the figure, the vertices of right triangle MLN are on the circle and L is the center of the circle. If the area of the region created by lines ML, LN, and arc MN is 9π, what is the area of the shaded region?
- A. 9π – 6
- B. 9π – 9
- C. 9
- D. 18
Correct Answer: D
Explanation:
The answer is D
Because the area of part of a circle is given, you need to determine what fraction of the circle is represented by that sector. The interior angle of the sector is 90°, which means that the area of the sector is 
of the area of the circle. Thus, multiply 9π by 4 to get 36π for the area of the circle. Now, solve for the radius, since the sides of the triangle are radii: 36π = π(r)2, so r = 6. The area of a triangle is 
bh = (6)(6) = 18.