Flashcard 14 - Math Reasoning Flashcard Set for the GED Test

The ratio of the areas of two similar triangles is equal to the reduced ratio of the squares of their corresponding sides.

Triangles A and B are similar. Triangle A has a base of 6 cm and height of 3 cm. Triangle B has a base of 10 cm and height of 5 cm.

Area of Triangle A: \(A_1=\frac{1}{2} \cdot 6 \cdot 3 = 9\)

Area of Triangle B: \(A_2=\frac{1}{2} \cdot 10 \cdot 5 = 25\)

Notice that: \(\frac{A_1}{A_2} = \frac{9}{25} = \frac{3^2}{5^2}\)