In triangle ABC, D is the midpoint of AC, and E is the midpoint of AB. Find the ratio of the area of trapezoid BCDE to the area of triangle ABC.

Guest Jun 30, 2020

#1**0 **

In triangle(ABC), D is the midpoint of AC, E is the midpoint of AB, and F is the midpoint of BC.

Construct DE, DF, and EF.

There are 4 congruent triangles: triangle(AED), triangle(EBF), triangle(DFC), and triangle(FDE).

Since all congruent triangles have equal areas, the area of triangle(ABC) is one-third the area of trapezoid(BCDE).

geno3141 Jun 30, 2020