Question

rectangles e and f are similar. if the area of rectangle e is 12, what is the area of rectangle f?
rectangle e: top side length 6, area = 12
rectangle f: top side length 5.4

Explanation:

Step1: Find the scale factor

The length of Rectangle E is 6, and the length of Rectangle F is 5.4. The scale factor \( k \) from E to F is \( \frac{5.4}{6} = 0.9 \).

Step2: Recall the relationship for areas of similar figures

For similar figures, the ratio of their areas is the square of the scale factor. Let \( A_E \) be the area of E and \( A_F \) be the area of F. So \( \frac{A_F}{A_E} = k^2 \).

Step3: Calculate the area of F

We know \( A_E = 12 \) and \( k = 0.9 \), so \( k^2 = 0.81 \). Then \( A_F = A_E \times k^2 = 12 \times 0.81 = 9.72 \).

Answer:

The area of rectangle F is \( 9.72 \).