SOLUTION: In the diagram, the area of triangle ABC is 48 cm^2 and DE and FG are perpendicular to BC. The area of pentagon ADEGF, is: A) 30 B) 42 C) 34 D) 36 E) 32 https://imageshack.

Question 1167550: In the diagram, the area of triangle ABC is 48 cm^2 and DE and FG are perpendicular to BC. The area of pentagon ADEGF, is:
A) 30
B) 42
C) 34
D) 36
E) 32
https://imageshack.com/i/pntQQVi7j

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Let H be on BC so that AH is perpendicular to BC. Then

(1) BED and BHA are similar triangles with scale factor 1:2, so the area of BED is 1/4 the area of BHA;
(2) CGF and CHA are similar triangles with scale factor 1:2, so the area of CGF is 1/4 the area of CHA

That makes the area of ADEGF 3/4 the area of ABC.

ANSWER: D: 3/4 of 48 cm^2 = 36cm^2

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