SAT Math Multiple Choice Practice Question 568: Answer and Explanation

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Question: 568

4.

In the figure above, ?ACE is equilateral, and B, D, and F are the midpoints of , , and , respectively. If the area of ?ACE is 24, what is the area of the shaded region?

A. 4
B. 6
C. 8
D. 12
E. 16

Correct Answer: B

Explanation:

B Because the triangle is equilateral, and each of the three sides is cut in half, all of the short segments in the triangle are equal. This means that all four triangles within the larger triangle are equilateral and congruent. Since one of the four triangles is shaded, the shaded area is of the area of the larger triangle. × 24 = 6, answer B.

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