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: 8 cm, 25 cm², 10 cm
prism b: 24 cm

Explanation:

Step1: Find the scale factor

The length of Prism A is 8 cm and Prism B is 24 cm. The scale factor \( k \) is \( \frac{24}{8}=3 \).

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 \( 10\times3 = 30 \) cm.

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

For similar figures, the ratio of areas is the square of the scale factor. The area of Prism A's trapezoid face is \( 25 \, \text{cm}^2 \). The ratio of areas is \( k^2=3^2 = 9 \). So the area of Prism B's trapezoid face is \( 25\times9=225 \, \text{cm}^2 \).

Answer:

Missing side length: 30 cm, Area of trapezoid face: \( 225 \, \text{cm}^2 \)