Question

1. both trapezoids are similar. the area of the larger trapezoid is 61 ft². which is the best approximation for the area of the smaller trapezoid?

options: 49 ft², 34 ft², 39 ft², 44 ft²

Explanation:

Step1: Find the scale factor

The heights of the trapezoids are 30 ft (larger) and 24 ft (smaller). Scale factor $k = \frac{24}{30} = \frac{4}{5}$.

Step2: Relate areas using scale factor

Area ratio = $k^2 = (\frac{4}{5})^2 = \frac{16}{25}$.

Step3: Calculate smaller area

Let $A_s$ = smaller area, $A_l$ = 61 ft².
$A_s = A_l \times \frac{16}{25} = 61 \times 0.64 ≈ 39$ ft².

Answer:

39 ft²