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
The lateral surface area of a pentagonal prism can be found by calculating the area of each of the five rectangular sides and then adding them together.
Each rectangular side has a length of 6 feet and a height equal to the perpendicular height of the pentagon, which is 5 feet. Therefore, the area of each side is:
Area = 6 feet * 5 feet = 30 square feet
There are a total of 5 rectangular sides, so the total lateral surface area is:
Total Area = 5 * 30 square feet = 150 square feet
Therefore, the lateral surface area of the regular pentagonal prism represented by the given net is 150 square feet.