SSAT Math Question 375: Answer and Explanation

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Question: 375

3.

In the figure, P is the center of the circle, and triangle QPR is a right triangle with vertices Q and P on the circle. If the circumference of the circle is 12π, what is the area of the shaded region?

  • A. 36 – 18π
  • B. 18π – 36
  • C. 9π – 18
  • D. 18 – 9π

Correct Answer: C

Explanation:

C

Questions seeking the area of a weird shaded region generally require you to subtract the area of one normal shape from the area of another normal shape. In this case, subtract the area of the triangle from the area of the quarter circle. The area of a quarter circle is πr2, but we need to find the radius from the circumference. As C = 2πr = 12π, the radius is 6. Now find the area of the quarter circle: π(6)2 = 9π. As the triangle is a right triangle, the radii are also the base and height. The area of a triangle is bh = (6)(6) = 18. Choice (C) reflects the difference between the two areas.

You can estimate

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