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
1,462.80 ft.2
1,462.80 ft. squared
1,215.60 ft.2
To calculate the surface area of the triangular prism-shaped tent, we need to find the areas of all individual faces and then add them up.
1. Calculate the area of the triangular base:
Area = 0.5 x base x height
Area = 0.5 x 20 ft x 9 ft
Area = 90 ft²
2. Calculate the area of the rectangular sides:
Area = 2 x length x height
Area = 2 x 24 ft x 9 ft
Area = 432 ft²
3. Calculate the area of the triangular sides (using Heron's formula to calculate the area of an isosceles triangle):
a = 20 ft, b = 20 ft, c = 13.45 ft
s = (20 + 20 + 13.45) / 2 = 26.725
Area = sqrt(26.725 x (26.725 - 20) x (26.725 - 20) x (26.725 - 13.45)) = 150.38 ft² (for one of the triangular sides, multiply by 2 to include both sides)
4. Add up all areas:
90 ft² (triangular base) + 432 ft² (rectangular sides) + 2 * 150.38 ft² (triangular sides) = 982.76 ft²
Therefore, the surface area of the triangular prism-shaped tent is approximately 982.76 ft².