SOLUTION: In the diagram, the ratio of the areas of △BED:△DFC is 1:4. If the area of △ABC is 84 cm^2, then the area of parallelogram AEDF, in cm^2 is... A) 36 and 1/4 B) 39 and 2/3

Question 1188319: In the diagram, the ratio of the areas of △BED:△DFC is 1:4. If the area of △ABC is 84 cm^2, then the area of parallelogram AEDF, in cm^2 is...
A) 36 and 1/4 B) 39 and 2/3 C) 40 and 3/4 D) 37 and 1/3 E) 38 and 1/3
https://ibb.co/YcFWXMT
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Here is a re-drawing of the given figure:

Given the parallel segments, we know triangles BED and DFC are similar; and knowing that the area of triangle DFC is 4 times the area of triangle BED, we know DC is twice BD.

Then we can draw several other segments parallel to the sides of triangle ABC...

... to see that triangle ABC can be divided into 9 congruent triangles.

Parallelogram AEDF is composed of 4 of those triangles, so its area is 4/9 of the area of triangle ABC.

84(4/9) = 28(4/3) = 112/3 = 37 1/3

ANSWER: D

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