Problem:
The shaded area formed by the two intersecting perpendicular rectangles, in square units, is
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Answer Choices:
A.
B.
C.
D.
E. unable to be determined from the information given
Solution:
The total shaded area is the sum of the areas of the "horizontal" rectangle and the "vertical" rectangle minus the area of the "overlapping" rectangle that is part of both of the other rectangles. Thus the desired area is .
"Slide" the rectangles as shown in the figure on the right so they form an L-shaped figure. We see that the shaded area is or or .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions