Help me please!!!!!!!!!!!

Question

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 30cm²?     

Answer 1

Without drawing:

1) small and big trianles are similar with the scaling coefficient 4

2) Marking DE length as a, the base of the big triangle is 4a

3) Marking the height of the small triangle as h, the height of the big triangle is 4h, and so the height of the trapezoid is 3h

4) Area of trapezoid is (a+4a)/2 * 3h = 30

You could find from it that a*h = 4

5) The area of the big triangle is 4a*4h/2 = 8(ah) = 8*4 = 32