The area of the triangle ABC is 68, DE is the middle line, parallel to the side AB. Find the area CDE.

In triangles ABC and CDE, the sides DE and AB are parallel, then the angle CDE is equal to the angle CAB as the corresponding angles at the intersection of these parallel secant AC.

The angle at the vertex C is common for the triangles, then the triangles ABC and CDE are similar in two angles.

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

The areas of similar triangles are referred to as the squared coefficient of similarity.

Sde / Savs = 1/4.

Sde = Savs / 4 = 68/4 = 17 cm2.

Answer: The area of the triangle SDE is 17 cm2.

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