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 a 1462.80ft^2
b 1215.60ft^2 c1305.60ft^2 d 982.8ft^2
To calculate the surface area of the triangular prism-shaped tent, we need to find the area of the triangles on both ends, the area of the three rectangular sides, and the area of the two parallelogram-shaped sides.
1. Area of the two triangular ends:
Each end is a right triangle with the base and height given. The area of one triangle is 0.5 * base * height.
Area of one end = 0.5 * 24 ft. * 9 ft. = 108 ft^2
Area of both ends = 2 * 108 ft^2 = 216 ft^2
2. Area of the three rectangular sides:
The tent has three rectangular sides: a 20 ft. by 9 ft. side, a 24 ft. by 9 ft. side, and a 24 ft. by 20 ft. side.
Area of side 1 = 20 ft. * 9 ft. = 180 ft^2
Area of side 2 = 24 ft. * 9 ft. = 216 ft^2
Area of side 3 = 24 ft. * 20 ft. = 480 ft^2
Total area of the three rectangular sides = 180 ft^2 + 216 ft^2 + 480 ft^2 = 876 ft^2
3. Area of the two parallelogram-shaped sides:
The two triangular ends are connected by two parallelogram-shaped sides, which can be calculated by finding the base (24 ft.) and height (13.45 ft.) of the trapezoid.
Area of one parallelogram side = 24 ft. * 13.45 ft. = 322.8 ft^2
Area of both parallelogram sides = 2 * 322.8 ft^2 = 645.6 ft^2
Finally, add all these areas together to get the total surface area of the tent:
Total surface area = 216 ft^2 (triangular ends) + 876 ft^2 (rectangular sides) + 645.6 ft^2 (parallelogram sides) = 1737.6 ft^2
Therefore, none of the provided options are correct. The correct surface area of the triangular prism-shaped tent is 1737.6 ft^2.