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) Responses 982.8 ft.2 982.8 ft. squared 1,305.60 ft.2 1,305.60 ft. squared 1,215.60 ft.2 1,215.60 ft. squared 1,462.80 ft.2 1,462.80 ft. squared
To calculate the surface area of the triangular prism shaped tent, we need to find the areas of the three faces: two triangular faces and one rectangular face.
1. Calculate the area of the two triangles:
Area = (1/2) * base * height
Area = (1/2) * 20 ft. * 9 ft. = 90 ft.2
Area = (1/2) * 24 ft. * 9 ft. = 108 ft.2
2. Calculate the area of the rectangular face:
Area = length * width
Area = 24 ft. * 20 ft. = 480 ft.2
3. Add up the areas of the three faces:
Total surface area = 90 ft.2 + 108 ft.2 + 480 ft.2 = 678 ft.2
Therefore, the surface area of the triangular prism shaped tent is 678 ft.2. None of the provided options match this result exactly, but the closest one is 1,305.60 ft.2 which is most likely a mistake in the options provided.