SSAT Math Question 605: Answer and Explanation
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Question: 605
16. 
In the figure above, the length of side AB of square ABCD is equal to 4 and the circle has a radius of 2. What is the area of the shaded region?
- A. 4 - π
- B. 16 - 4π
- C. 8 + 4π
- D. 4π
Correct Answer: B
Explanation:
Take this question in bite-sized pieces. The question asks for the shaded region, so you want the part inside the square but outside the circle. In other words, if you find the area of the square and the area of the circle, you can find the shaded region by removing what you do not need (the area of the circle). First, find the area of the square. The side of the square is equal to 4, so A = s2 = 42 = 16. Eliminate (A), (C), (D), and (E), since these do not contain 16. For added security, find the area of the circle. The radius is 2, so A = πr2 = π(2)2 = 4π. Remember to subtract that from the area of the square, so the full answer is 16 - 4π. The correct answer is (B).