GRE Problem Solving Explanation

10. Rectangle ABCD has a perimeter of 26. The half circle with diameter AD has an area of 8π. What is the perimeter of the part of the figure that is not shaded?

A. 26 + 4π
B. 18 + 8π
C. 18 + 4π
D. 14 + 4π
E. 14 + 2π

Correct Answer: C

Explanation:

The total perimeter of the un-shaded part is made up of three sides of the rectangle and the perimeter of the half-circle.
The area of a half circle = ½ π r²
8 π = ½ π r²; therefore r = 4
The perimeter of the half circle is ½ 8 π = 4 π
The diameter of the circle (8) = the length of the rectangle.
Total perimeter of the rectangle = 26
Three sides measure 26 - 8 = 18     Ans. 18 + 4π

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