In △ABC a line segment DE connects sides AB and BC so that DE ∥ AC. The lengths of the sides of △DBE are four times shorter than the lengths of the sides of △ABC. What is the area of △ABC if the area of a trapezoid ADEC is 30cm^2?

32 cm^2

Step-by-step explanation:

The sides of ∆DBE or 1/4 of the sides of ∆ABC, so its area is (1/4) ^2 = 1/16 of the area of ∆ABC. The trapezoid's area is then 1 - 1/16 = 15/16 of the total area of ∆ABC. Said another way, the area of ∆ABC is 16/15 times the area of the trapezoid.

Area ∆ABC = (16/15) · (30 cm^2) = 32 cm^2