Line segment MN is the middle line of triangle ABC, parallel to side AB. The area of triangle AMN is 21

Line segment MN is the middle line of triangle ABC, parallel to side AB. The area of triangle AMN is 21. Find the area of triangle ABC.

In the resulting triangle ACN, NM is the median of this triangle, since point M is the middle of AC. The median divides the triangle into two equal triangles. By condition, Samn = 21 cm2, which means that Snmc is the same equal to 21 cm2.

In triangle ABC, AN will also be the median, since point N is the middle of CB and it divides triangle ABC into two equal triangles Sanb = Sanc.

Sanc = Samn + Snmc = 21 + 21 = 42 cm2. Then Sabc = Sanc + Sanb = 42 + 42 = 84 cm2.

Answer: Sabc = 84 cm2.