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
To find the lateral surface area of the pentagonal prism, we need to calculate the area of all five rectangles on the sides and then add the area of the two pentagons on the top and bottom.
Each of the five rectangles has a base of 4 feet and a height of 6 feet, so the area of one rectangle is 4 feet * 6 feet = 24 square feet. Since there are five rectangles, the total area of the rectangles is 5 * 24 = 120 square feet.
The area of one pentagon can be calculated using the formula for the area of a regular pentagon: A = (1/2) * Perimeter * Apothem. The perimeter of the pentagon is 5 * 4 = 20 feet, and the apothem is given as 5 feet. Therefore, the area of one pentagon is (1/2) * 20 feet * 5 feet = 50 square feet. Since there are two pentagons, the total area of the pentagons is 2 * 50 = 100 square feet.
Therefore, the lateral surface area of the regular pentagonal prism is the sum of the areas of the rectangles and the pentagons: 120 square feet + 100 square feet = 220 square feet.
So, the lateral surface area of the pentagonal prism represented by the given net is 220 square feet.