Question

6 cm 8 cm 9 cm find the total surface area of the rectangular prism in the figure. a) 522 cm² b) 432 cm² c) 348 cm² d) 174 cm² question 10 (5 points) listen image of a landscape with a dock, boat, and measurements 156 ft, 90 ft

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 \( S = 2(lw + lh + wh) \).

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

From the figure, we have \( l = 8 \, \text{cm} \), \( w = 6 \, \text{cm} \), and \( h = 9 \, \text{cm} \).

Step3: Substitute the values into the formula.

First, calculate \( lw \), \( lh \), and \( wh \):

• \( lw = 8 \times 6 = 48 \, \text{cm}^2 \)
• \( lh = 8 \times 9 = 72 \, \text{cm}^2 \)
• \( wh = 6 \times 9 = 54 \, \text{cm}^2 \)

Then, substitute these into the surface area formula:
\( S = 2(48 + 72 + 54) \)

Step4: Simplify the expression inside the parentheses.

\( 48 + 72 + 54 = 174 \)

Step5: Multiply by 2.

\( S = 2 \times 174 = 348 \, \text{cm}^2 \)

Answer:

C) \( 348 \, \text{cm}^2 \)