Question

find the surface area of a rectangular prism with base 5 m by 2 m and height 8 m.
a. 15 m² \tc. 80 m²
b. 30 m² \td. 132 m²

please select the best answer from the choices provided

○ a
○ b
○ c
○ d

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 \( SA = 2(lw + lh + wh) \). Here, \( l = 5 \, \text{m} \), \( w = 2 \, \text{m} \), and \( h = 8 \, \text{m} \).

Step2: Calculate each term inside the parentheses

First, calculate \( lw \): \( lw = 5 \times 2 = 10 \, \text{m}^2 \).
Next, calculate \( lh \): \( lh = 5 \times 8 = 40 \, \text{m}^2 \).
Then, calculate \( wh \): \( wh = 2 \times 8 = 16 \, \text{m}^2 \).

Step3: Sum the terms and multiply by 2

Sum the three terms: \( lw + lh + wh = 10 + 40 + 16 = 66 \, \text{m}^2 \).
Multiply by 2: \( SA = 2 \times 66 = 132 \, \text{m}^2 \).

Answer:

d. \( 132 \, \text{m}^2 \)