Question

1. the dimensions of a rectangular prism is shown in the diagram.

what is the total surface area of the prism?
a. 123.8 square inches
b. 132.13 square inches
c. 54.4 square inches

Explanation:

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

The formula for the total surface area \( S \) of a rectangular prism with length \( l \), width \( w \), and height \( h \) is \( S = 2(lw + lh + wh) \).
Here, \( l = 10.2 \) in, \( w = 3.4 \) in, and \( h = 2 \) in.

Step2: Calculate each term inside the parentheses

• Calculate \( lw \): \( lw = 10.2\times3.4 = 34.68 \)
• Calculate \( lh \): \( lh = 10.2\times2 = 20.4 \)
• Calculate \( wh \): \( wh = 3.4\times2 = 6.8 \)

Step3: Sum the terms and multiply by 2

First, sum the terms: \( 34.68 + 20.4 + 6.8 = 61.88 \)
Then, multiply by 2: \( S = 2\times61.88 = 123.76 \approx 123.8 \) (rounded to one decimal place)

Answer:

A. 123.8 square inches