The area of the triangle ABC is equal to 124. DE is the middle line. Find the area of the CDE triangle.

To solve the problem, consider the figure.

Since the middle line DE of triangle ABC is parallel to the base AB, and the angle at the vertex C is common for triangles ABC and DEC, then triangles ABC and DEC are similar triangles.

Since the middle line of a triangle is half the length of the base of the triangle, the coefficient of similarity of these triangles will be:

K = AB / DE = 2.

The ratio of the areas of similar triangles is equal to the squared coefficient of similarity of these triangles.

SABC / SCDE = K ^ 2 = 4.

SCDE = SABC / 4 = 124/4 = 31 cm2.

Answer: SCDE = 31 cm2.