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)
The lateral surface area of a regular pentagonal prism can be calculated by finding the area of each of the five rectangles that make up the sides of the prism, and then adding them up.
The lateral surfaces of the prism are the five rectangles on the sides of the prism. Each rectangle has a base of 6 feet (the height of the prism) and a height of 4 feet (the side length of the pentagon). So the lateral surface area of one rectangle is:
Area = base x height
Area = 6 feet x 4 feet
Area = 24 square feet
Since there are five identical rectangles making up the lateral surface of the prism, the total lateral surface area is:
Total Area = 5 x Area
Total Area = 5 x 24 square feet
Total Area = 120 square feet
Therefore, the lateral surface area of the regular pentagonal prism represented by the given net is 120 square feet.