Sum of areas of two triangles

Geometry Level 2

In the diagram shown above, A C AC is parallel to E D ED and A B D E ABDE is a parallelogram such that A B = E D AB=ED and A E = B D AE=BD . Given that A B = 10 AB=10 and A F = 7 AF=7 , find the sum of the areas of A D E \triangle ADE and E C D \triangle ECD .


The answer is 70.

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1 solution

If a parallelogram has the same base as a triangle, and they are between the same parallel lines, the area of the parallelogram is twice the area of the triangle. In the problem, the area of the parallelogram is 10 7 = 70 10\cdot 7=70 . Since the area of A D E = 35 \triangle ADE=35 and E C D = 35 \triangle ECD=35 , the desired answer is 35 + 35 = 70 35+35=70 .

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