Question

the figures below are similar. the labeled sides are corresponding.

$a_1 = 3\text{ yd}^2$

$a_2 = ?$

what is the area of the larger rectangle?

$a_2 = \square$ square yards

Explanation:

Step1: Find the scale factor

The corresponding sides of the similar rectangles are 1 yd (small) and 3 yd (large). So the scale factor \( k=\frac{3}{1} = 3\).

Step2: Relate areas of similar figures

For similar figures, the ratio of areas is the square of the scale factor. Let \( A_1\) be the area of the small rectangle and \( A_2\) be the area of the large rectangle. Then \(\frac{A_2}{A_1}=k^{2}\).

Step3: Calculate \( A_2\)

We know \( A_1 = 3\space yd^{2}\) and \( k = 3\), so \( k^{2}=9\). Then \( A_2=A_1\times k^{2}=3\times9 = 27\).

Answer:

27