Question

two similar three - dimensional prisms are shown in the image. prism a displays the measurements of the length and width of the base, along with the area of the front trapezoid face. for prism b, determine the corresponding missing side length and the area its corresponding front trapezoid face.
prism a: 25 cm², 10 cm, 8 cm
prism b: 24 cm
options: 30 cm, 26 cm, 225 cm², 75 cm²

Explanation:

Step1: Find the scale factor

The corresponding base lengths of Prism A and Prism B are 8 cm and 24 cm. The scale factor \( k \) is calculated as \( \frac{24}{8} = 3 \).

Step2: Find the missing side length of Prism B

The side length of Prism A is 10 cm. Using the scale factor, the missing side length of Prism B is \( 10 \times 3 = 30 \) cm.

Step3: Find the area of the front trapezoid face of Prism B

For similar figures, the ratio of areas is the square of the scale factor. The area of the front trapezoid face of Prism A is \( 25 \, \text{cm}^2 \). The scale factor squared is \( 3^2 = 9 \). So the area of Prism B's front trapezoid face is \( 25 \times 9 = 225 \, \text{cm}^2 \).

Answer:

The missing side length of Prism B is 30 cm, and the area of its front trapezoid face is \( 225 \, \text{cm}^2 \).