A regular decagon is a shape with 10 sides of identical length. A piece of chimney pipe has open ends shaped like decagonal bases with sides that are 6.5 inches. The prism is 18 inches tall. What area of aluminum is needed to construct this piece of chimney?
1053 in2
1287 in²
1170 in2
936 in2
To find the area of the aluminum needed to construct the chimney piece, we need to find the lateral surface area of the prism. The lateral surface area of a prism can be found by multiplying the perimeter of the base by the height.
The perimeter of a decagon can be found by multiplying the number of sides (10) by the length of each side (6.5 inches).
Perimeter of the base = 10 * 6.5 inches = 65 inches
Now, multiply the perimeter of the base by the height of the prism to find the lateral surface area:
Lateral surface area = 65 inches * 18 inches = 1170 square inches
Therefore, the area of aluminum needed to construct this piece of chimney is 1170 in².
So, the correct answer is 1170 in2.