SAT Math Multiple Choice Practice Question 526: Answer and Explanation

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Question: 526


In the figure above, ABCD is a square with sides of length 2. The square contains two semicircles with diameters and . What is the sum of the areas of the two shaded regions?

B. 2 – π
C. 4 – π
D. 4 – 2π

Correct Answer: C


C Choices B and D have negative values, so you can eliminate them right away. Start with the area of the whole figure. The square has sides of 2, so its area is 4. Now let's remove the area of the two semicircles (which is the same as the area of one whole circle). These semicircles have a radius of 1, so the area of one whole circle will be π. So the area of the shaded region will be 4 – π.

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