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Question

Lateral Surface Area Practice
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Question
Use the image to answer the question.

An illustration shows an unfolded version of a pentagonal prism.
A horizontal rectangle is divided into five segments of vertical length 6 feet. The segments are divided with dashed lines. Two pentagons adjoin the top and bottom sides of the second rectangle, also with common dashed lines. Each side of the pentagon is 4 feet. The perpendicular height of the pentagon is drawn with a dotted line extending from the from the center of a side to the center of the pentagon, and is labeled as 5 feet. A right angle symbol is shown where the perpendicular height meets the side.

Find the lateral surface area for the regular pentagonal prism represented by the given net.

(1 point)
ft.2

Answer 1

To find the lateral surface area of the pentagonal prism, you can use the formula for the lateral surface area of a prism:

\[ \text{Lateral Surface Area} = \text{Perimeter of the base} \times \text{Height} \]

Step 1: Find the perimeter of the pentagonal base.

A regular pentagon has 5 equal sides, and each side is given as 4 feet. Therefore, the perimeter \( P \) is:

\[ P = 5 \times \text{side length} = 5 \times 4 \text{ ft} = 20 \text{ ft} \]

Step 2: Determine the height of the prism.

The height of the prism is given as 6 feet.

Step 3: Calculate the lateral surface area.

Now, plug the values into the lateral surface area formula:

\[ \text{Lateral Surface Area} = P \times \text{Height} = 20 \text{ ft} \times 6 \text{ ft} = 120 \text{ ft}^2 \]

Thus, the lateral surface area of the regular pentagonal prism is 120 ft².