2006 UNCO Math Contest II Problems/Problem 5
In the figure is parallel to and also is parallel to . The area of the larger triangle is . The area of the trapezoid is . Determine the area of triangle .
Since we know is equal to the short side of both triangles and that is equal to the long sides of the hypotenuse of the triangle. Thus we know that if we make a line (as seen below), all four triangles in are congruent.
Then, since we know the sum of all four triangles is , we can solve the easy division problem and see that the area of
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