The area of triangle ABC is 24. DE is the middle line. find the area of the trapezoid ABDE.

1. The middle line DE splits triangle ABC into trapezoid ABDE and triangle EDC. Triangles ABC and EDC are similar with coefficient k = 2, since DE is the middle line of triangle ABC.

The areas of similar triangles are related to each other like the squared coefficient. Let’s write down:

Sm / Sb = k ^ 2.

Find the area of the triangle EDC (Smb):

Sm / 24 = 2 ^ 2;

Sм / 24 = 4;

Sм = 6.

2. Find the area of the trapezoid ABDE:

24 – 6 = 18.

Answer: the area of the trapezoid is ABDE 18.