Question

use the net to find the surface area of the rectangular prism. 5 ft 15 ft 4 ft 4 ft 5 ft 15 ft a 200 ft² b 310 ft² c 340 ft² d 390 ft²

Explanation:

Step1: Identify the three pairs of faces

A rectangular prism has 3 pairs of congruent faces. The dimensions of the pairs are: length - width ($l = 15$ ft, $w=5$ ft), length - height ($l = 15$ ft, $h = 4$ ft), and width - height ($w = 5$ ft, $h=4$ ft).

Step2: Calculate the area of each pair of faces

The area of the length - width pair is $2\times(l\times w)=2\times(15\times5)=150$ square feet. The area of the length - height pair is $2\times(l\times h)=2\times(15\times4) = 120$ square feet. The area of the width - height pair is $2\times(w\times h)=2\times(5\times4)=40$ square feet.

Step3: Sum up the areas of all pairs

The surface area $S$ of the rectangular prism is $S=150 + 120+40=310$ square feet.

Answer:

B. $310$ ft²