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
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To find the lateral surface area of the pentagonal prism, we need to find the area of each of the five rectangular faces and two pentagonal faces.
Each rectangular face has a length of 6 feet and a width of 4 feet, so the area of each rectangular face is 6 ft * 4 ft = 24 ft^2. Since there are five rectangular faces, the total area of the rectangular faces is 5 * 24 ft^2 = 120 ft^2.
Each pentagonal face has a base of 4 feet and a height of 5 feet, so the area of each pentagonal face is (1/2) * 4 ft * 5 ft = 10 ft^2. Since there are two pentagonal faces, the total area of the pentagonal faces is 2 * 10 ft^2 = 20 ft^2.
Therefore, the total lateral surface area of the regular pentagonal prism is 120 ft^2 + 20 ft^2 = 140 ft^2.