SAT Math Multiple Choice Practice Question 176: Answer and Explanation

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Question: 176


The drawing above shows four identical triangles surrounding a smaller square. Given that AB = 10, find the area of the square.

C. 25
E. 50

Correct Answer: B


B. The four triangles themselves must form a square, and the area of this square is just 10 × 10 = 100. The triangle at the top is a 30-60-90 triangle, and the pattern for these -triangles tells you that the missing sides must be 5 and , which makes the area of this triangle . Because the drawing includes four copies of this triangle, the four together have an area of . After all that work, all that's left is subtraction, and you end up with Choice (B).

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