Triangles ABC and FDG are similar. The similarity coefficients of these triangles are 2/3

Triangles ABC and FDG are similar. The similarity coefficients of these triangles are 2/3 Find the area of triangle FDG if the area of triangle ABC is 18 cm2.

Let the area of the triangle ABC be S1 = 18 cm square, then the area of the triangle FDG is S2.
The ratio of the areas of similar triangles is equal to the square of the similarity coefficient, then:
S1 / S2 = (2/3) ^ 2;
18 / S2 = 4/9;
S2 = 18 * 9/4 = 9 * 9/2 = 81/2 = 40.5 (cm square).
Answer: S FDG = 40.5 cm square.