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
1,305.60 ft.2
1,305.60 ft. squared
1,215.60 ft.2
1,215.60 ft. squared
982.8 ft.2
982.8 ft. squared
1,462.80 ft.2
To calculate the surface area of a triangular prism shaped tent, we need to calculate the surface area of the two triangular faces and the three rectangular faces separately.
1. Calculate the surface area of the two triangular faces:
Each triangular face has an area of (1/2) * base * height. The base of the triangle is the width of the tent and the height is the height of the tent.
Area of one triangular face = (1/2) * 20 ft * 9 ft = 90 ft²
Total surface area of two triangular faces = 2 * 90 ft² = 180 ft²
2. Calculate the surface area of the three rectangular faces:
Each rectangular face has an area of length * height.
Area of one rectangular face (side 1) = 24 ft * 9 ft = 216 ft²
Area of the other two rectangular faces (sides 2 and 3) = 20 ft * 9 ft = 180 ft²
Total surface area of the three rectangular faces = 216 ft² + 180 ft² = 396 ft²
3. Total surface area of the triangular prism shaped tent:
Add the surface area of the two triangular faces and the three rectangular faces.
Total surface area = 180 ft² (triangular faces) + 396 ft² (rectangular faces) = 576 ft²
Therefore, the surface area of the triangular prism shaped tent is 576 ft².
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
1,305.60 ft.2
1,305.60 ft. squared
1,215.60 ft.2
1,215.60 ft. squared
982.8 ft.2
982.8 ft. squared
1,462.80 ft.2 choose from the list
To calculate the surface area of a triangular prism shaped tent, we first need to calculate the area of the triangular ends and the lateral surface area of the prism.
1. Area of the triangular ends:
Since the triangle is a right triangle, we can use the formula for the area of a right-angled triangle:
Area = (1/2) * base * height
Area = (1/2) * 20 ft * 9 ft = 90 ft²
Since there are two triangular ends, the total area of the two ends is 2 * 90 ft² = 180 ft².
2. Lateral surface area of the prism:
To calculate the lateral surface area (the three rectangular sides), we need to first calculate the perimeter of the base of the prism:
Perimeter = width + length + hypotenuse
Perimeter = 20 ft + 24 ft + 13.45 ft = 57.45 ft
Now, we can calculate the lateral surface area of the prism:
Lateral surface area = perimeter * height
Lateral surface area = 57.45 ft * 9 ft = 517.05 ft²
3. Total surface area:
The total surface area of the prism is the sum of the area of the two triangular ends and the lateral surface area:
Total surface area = 180 ft² (triangular ends) + 517.05 ft² (lateral surface area) = 697.05 ft²
Therefore, the surface area of the triangular prism shaped tent is approximately 697.05 ft². Since this value is not an option provided, the closest option is 1,462.80 ft².