alculate 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)
Responses
1,462.80 ft.2
1,462.80 ft. squared
982.8 ft.2
982.8 ft. squared
1,305.60 ft.2
1,305.60 ft. squared
1,215.60 ft.2
To calculate the surface area of the triangular prism tent, we need to find the area of each face and then sum them up.
First, let's find the area of the triangular ends of the tent:
- The base of the triangle is 20 ft and the height is 9 ft.
- Area = 0.5 x base x height = 0.5 x 20 x 9 = 90 ft^2 (for each end)
- Total area of the two ends = 90 ft^2 + 90 ft^2 = 180 ft^2
Next, let's find the area of the rectangular sides of the tent:
- The length is 24 ft, the height is 9 ft, and the width is 13.45 ft (the hypotenuse).
- Area = perimeter of rectangle x height = (2 x length + 2 x width) x height = (2 x 24 + 2 x 13.45) x 9 = (48 + 26.9) x 9 = 74.9 x 9 = 674.1 ft^2 (for each side)
- Total area of the two sides = 674.1 ft^2 + 674.1 ft^2 = 1348.2 ft^2
Finally, sum up the areas of the ends and sides to find the total surface area:
- Total surface area = 180 ft^2 (ends) + 1348.2 ft^2 (sides) = 1528.2 ft^2
Therefore, the surface area of the triangular prism-shaped tent is 1528.2 ft^2. None of the provided responses match this calculated value.