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Lengths are shown in inches on the drawing of the rectangle below. What is the shaded area, in square inches? A. 18 B. 24 C. 57 D. 78 E. 96 The correct answer is C. Explanation: The area of the shaded region is the area of the 8-by-12 rectangle minus the area of the right triangle with base 8 and height 9 minus the area of the right triangle with base 2 and height 12 – 9 = 3. So A = 8(12) – 1 (8)(9) – 1 (2)(3) = 96 – 36 – 3 = 57. 2 2 Check: The shaded region is a right triangle with base 8 and height 9 plus a trapezoid with parallel sides 8 and 8 – 2 = 6 and height 12 – 9 = 3. So A = 1 (8)(9) + 1 (8 + 6)(3) = 36 + 21 = 57. 2 2