Question

the figures below are similar. the labeled sides are corresponding.
6 ft
3 ft
a₁ = 36 ft² a₂ = ?
what is the area of the smaller square?
a₂ = square feet

Explanation:

Step1: Find the scale factor

The ratio of corresponding sides is $\frac{3}{6}=\frac{1}{2}$.

Step2: Relate areas of similar figures

For similar figures, the ratio of areas is the square of the ratio of corresponding sides. So the ratio of areas is $(\frac{1}{2})^2=\frac{1}{4}$.

Step3: Calculate the area of the smaller square

Let $A_2$ be the area of the smaller square. We know $A_1 = 36$ square feet. Since $\frac{A_2}{A_1}=\frac{1}{4}$, then $A_2=\frac{1}{4}\times A_1$. Substituting $A_1 = 36$, we get $A_2=\frac{1}{4}\times36 = 9$.

Answer:

9