Problem:
An isosceles right triangle with legs of length is partitioned into congruent triangles as shown. The shaded area is
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Answer Choices:
A.
B.
C.
D.
E.
Solution:
The area of each of the small shaded triangles is . There are ten of these, so the shaded area is .
The area of the large triangle is . Only of the small triangles are shaded. Thus the shaded area is of , or .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions