SAT Math Multiple Choice Practice Question 20: Answer and Explanation

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Question: 20

20.

Given that ABCD and BDEF are rectangles, find the shaded area in this diagram.

A. 24
B.
C. 20
D.
E. 16

Correct Answer: A

Explanation:

A. ABD is a right triangle, so you can find BD using the Pythagorean Theorem: (4)2 + (8)2 = c2; 16 + 64 = c2; 80 = c2; so c = . Because DE = , the area of BDEF is . Now, the shaded region's area is the area of the rectangle BDEF minus the area of the triangle CBD, and the area of CBD equals 1/2 × base × height = 1/2 × 8 × 4 = 16. Thus, the area of the shaded region is 40 - 16 = 24.

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