ISEE Mathematics Achievement Question 327: Answer and Explanation

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Question: 327

11.

PQRS is a square with an area of 144. What is the area of the shaded region?

A. 50
B. 72
C. 100
D. 120

Correct Answer: B

Explanation:

B Ballparking is one way to work through this problem. The shaded region looks to be about half the square, and half of 144 is 72, (B). To be more precise, the side of the square must be 12 since A = s² and 12² = 144, so the height of each shaded triangle is 12. The base for one triangle ends at P and the base for the other triangle ends at Q, and PQ = 12 since it's a side of the square. So make the base for each triangle 6 since the two bases must add up to 12. Plug those values into the formula: A = bh = (6)(12) = 36. Since both areas equal 36, the total area of the shaded region is 36 + 36 = 72. The correct answer is (B).

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