1992 AJHSME Problems/Problem 10
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Contents
Problem
An isosceles right triangle with legs of length is partitioned into
congruent triangles as shown. The shaded area is
Solution
Solution 1
Because the smaller triangles are congruent, the shaded area take of the largest triangles area, which is
, so the shaded area is
.
Solution 2
Each of the triangle has side length of , so the area is
. Because there are
triangles is the shaded area, its area is
.