Question

find the surface area of this rectangular prism. be sure to include the correct unit in your answer.
image of a rectangular prism labeled with 3 ft (height), 7 ft (length), 5 ft (width)
input box
unit options: ft, ft², ft³; reset and multiply buttons

Explanation:

Step1: Recall the formula for the surface area of a rectangular prism

The formula for the surface area \( SA \) of a rectangular prism with length \( l \), width \( w \), and height \( h \) is \( SA = 2(lw + lh + wh) \).

Step2: Identify the values of \( l \), \( w \), and \( h \)

From the diagram, we have \( l = 7 \) ft, \( w = 5 \) ft, and \( h = 3 \) ft.

Step3: Calculate each term inside the parentheses

First, calculate \( lw \): \( lw = 7\times5 = 35 \) square feet.
Next, calculate \( lh \): \( lh = 7\times3 = 21 \) square feet.
Then, calculate \( wh \): \( wh = 5\times3 = 15 \) square feet.

Step4: Sum the terms and multiply by 2

Sum the three terms: \( 35 + 21 + 15 = 71 \).
Then multiply by 2: \( SA = 2\times71 = 142 \) square feet.

Answer:

\( 142 \) square feet (or \( 142\ \text{ft}^2 \))