Question

Calculate the surface area of a triangular prism shaped

tent if the height is 9 ft., the length is 24 ft., the width is
20 ft., and the hypotenuse of the cover is 13.45 ft.
(1 point)
982.8 ft.
2
1, 462.80 ft.
2
1, 305.60 ft.
2
1, 215.60 ft.
2

Answer 1

[AI-generated answer — Bot GPT 3.5]

To calculate the surface area of the triangular prism shaped tent, we first need to find the surface area of the triangular sides and the rectangular sides separately.

1. Surface area of the triangular sides:
First, we need to calculate the base of the triangle. Using the Pythagorean theorem:
Base = sqrt(hypotenuse^2 - height^2)
Base = sqrt(13.45^2 - 9^2) = sqrt(180.9025 - 81) = sqrt(99.9025) = 9.99 ft

Now, we can calculate the area of one triangular side:
Area = (1/2) * base * height
Area = (1/2) * 9.99 * 9 = 44.955 ft^2

Since there are two triangular sides, the total surface area of the triangular sides is:
Total triangular surface area = 2 * Area = 2 * 44.955 = 89.91 ft^2

2. Surface area of the rectangular sides:
There are three rectangular sides to the tent. The total surface area of the rectangular sides is:
Total rectangular surface area = 2 * (length * width + height * length + height * width)
Total rectangular surface area = 2 * (24*20 + 9*24 + 9*20) = 2 * (480 + 216 + 180) = 2 * 876 = 1752 ft^2

Now, the total surface area of the tent is:
Total surface area = Total triangular surface area + Total rectangular surface area
Total surface area = 89.91 + 1752 = 1841.91 ft^2

Therefore, the surface area of the triangular prism shaped tent is approximately 1,841.91 ft^2.