The area of the triangle ABC is 98, the segment MN is the midline of the triangle, parallel to the side AB

The area of the triangle ABC is 98, the segment MN is the midline of the triangle, parallel to the side AB, find the area of the triangle CMN.

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

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

In triangles ABC and CMH, angle C is common, angle CAB = CHM, then triangles ABC and CMH are similar in two angles.

The coefficient of similarity of triangles is: K = MH / AB = 1/2.

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

Scmn / Savs = 1/4.

Scmn = Saavs / 4 = 98/4 = 24.5 cm2.

Answer: The area of the SMN triangle is 24.5 cm2.