In the triangle ABC, DE is the middle line. The area of the triangle CDE = 24. Find the area of the triangle ABC.

Since DE is the middle line of the triangle ABC, then DE is parallel to AB.

Then the angle CAB = CDE as the corresponding angles at the intersection of parallel straight lines DE and AB secant AC.

Angle ACB and DCE are common for triangles ABC and CDE, then triangles ABC and CDE are similar in two angles.

Since DE is the middle line, then DE = AB / 2, and the coefficient of similarity of triangles is: K = DE / AB = 1/2.

The area of similar triangles is referred to as the squared coefficient of similarity.

Sde / Savs = (1/2) 2 = 1/4.

Savs = 4 * Sde = 4 * 24 = 96 cm2.

Answer: The area of the triangle ABC is 96 cm2.