Geometry Puzzle – Challenge 59

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Geometry Puzzle – Challenge 59

Challenge:

In the figure above, ABCD is a parallelogram and point E is the midpoint of CD. What is the ratio of the area of triangle ADE to parallelogram ABCD?

A- 1 : 2

B- 1 : 3

C- 1 : 4

D- 1 : 6

E- it cannot be determined

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The correct answer is C.

AD divides the parallelogram in half. AE divides the half parallelogram into half again. Because the heights of triangles ACE and ADE are equal and their bases are equal.
Triangle ADE is, therefore, one fourth of the parallelogram. And the ratio is 1 : 4

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