SSAT Math Question 308: Answer and Explanation

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Question: 308

2. Isosceles triangle XYZ is inscribed in Circle O below as shown.

If the radius of the circle is 10, what is the area of the shaded region?

  • A. 25π – 50
  • B. 50π – 100
  • C. 50π – 200
  • D. 100π – 100

Correct Answer: B

Explanation:

The answer is B

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 semicircle. The area of a semicircle is πr2 = π(10)2 = 50π. Triangles formed by the endpoints of a diameter and part of a circle are always right triangles. Thus, the sides of the triangle are the base and height of the triangle. If you draw in a radius to split the triangle, you have formed two right triangles with sides length 10. Using the Pythagorean theorem, you can find the side of the larger triangle: . The ar

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