Surface Area of Right Rectangular Prisms Quick Check

Question

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Question
Use the formula for the surface area of a right rectangular prism to find the surface area of a shape with the following measurements: length = 4.5 cm, width = 3.5 cm, and height = 2.5 cm.(1 point)
Responses

35.75 cm2
35.75 cm squared

63 cm2
63 cm squared

71.5 cm2
71.5 cm squared

10.5 cm2

Answer 1

The formula for the surface area \( S \) of a right rectangular prism is given by:

\[ S = 2lw + 2lh + 2wh \]

where \( l \) is the length, \( w \) is the width, and \( h \) is the height.

Given:

• Length \( l = 4.5 \) cm
• Width \( w = 3.5 \) cm
• Height \( h = 2.5 \) cm

Now, substituting the values into the formula:

1. Calculate \( 2lw \): \[ 2lw = 2 \times 4.5 \times 3.5 = 31.5 \text{ cm}^2 \]

2. Calculate \( 2lh \): \[ 2lh = 2 \times 4.5 \times 2.5 = 22.5 \text{ cm}^2 \]

3. Calculate \( 2wh \): \[ 2wh = 2 \times 3.5 \times 2.5 = 17.5 \text{ cm}^2 \]

Now, add these results together to find the total surface area:

\[ S = 31.5 + 22.5 + 17.5 = 71.5 \text{ cm}^2 \]

Therefore, the surface area of the prism is \( 71.5 \text{ cm}^2 \).

The correct response is 71.5 cm².