Triangle ABC BC = 12, MN = 4 MN = 2 Find the area ABC

Let us prove that triangles ABC and AMН are similar.

The angle A for triangles is common, the angle AMН = ABC is as criss-crossing angles at the intersection of parallel straight lines BC and ML of the secant AB, then the triangles ABC and AMН are similar in two angles.

Let’s determine the coefficient of similarity of triangles.

K = MH / BC = 4/12 = 1/3.

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

Samn / Savs = 1/9.

Savs = 9 * Samn = 9 * 2 = 18 cm2.

Answer: The area of the triangle ABC is 18 cm2.