Lengths are shown in inches on the drawing of the rectangle below.

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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.
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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.
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