# SAT Math Multiple Choice Question 974: Answer and Explanation

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**Question: 974**

**10.**

Each of the three shaded regions above is a semicircle. If *AB* = 4, *BC* = 2*AB*, and *CD* = 2*BC*, what is the area of the entire shaded region?

- A. 28π
- B. 42π
- C. 84π
- D. 96π

**Correct Answer:** B

**Explanation:**

**B**

**Difficulty:** Medium

**Category:** Additional Topics in Math / Geometry

**Strategic Advice:** Use the only diameter given (*AB* = 4) to determine the other two diameters. Once there, use *A* = π*r*^{2} to find the area of each. Remember to multiply each area by to account for the fact that you have semicircles, not whole circles.

**Getting to the Answer:** The diameter of semicircle *AB* is given as 4, so its radius is 2. Therefore, the area of semicircle *AB* is. If *BC* = 2*AB*, then *BC* = 8, and the radius of semicircle *BC* is 4. Its area, therefore, is. Similarly, because *CD* = 2*BC*, *CD* must equal 16, and the radius of semicircle *CD* is 8, giving it an area of. Add the three areas together to get 2π + 8π + 32π = 42π, which matches (B).