Question

the figures below are similar. the labeled sides are corresponding.
4 ft
1 ft
a₁ = ? a₂= 1 ft²
what is the area of the larger square?
a₁ = square feet

Explanation:

Step1: Find the scale factor of sides

The side length of the larger square is \( 4 \) ft and the side length of the smaller square is \( 1 \) ft. The scale factor \( k \) of the sides is \( \frac{4}{1}=4 \).

Step2: Relate areas of similar figures

For similar figures, the ratio of their areas is the square of the ratio of their corresponding side lengths. If the area of the smaller square is \( A_2 = 1\) \( \text{ft}^2 \) and the area of the larger square is \( A_1 \), then \( \frac{A_1}{A_2}=k^2 \). Substituting \( k = 4 \) and \( A_2=1 \), we get \( \frac{A_1}{1}=4^2 \).

Step3: Calculate \( A_1 \)

Simplify \( 4^2 = 16 \), so \( A_1=16\times1 = 16 \) \( \text{ft}^2 \).

Answer:

\( 16 \)