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
1,462.80 ft.2
1,462.80 ft. squared
982.8 ft.2
982.8 ft. squared
1,215.60 ft.2
1,215.60 ft. squared
1,305.60 ft.2
To calculate the surface area of a triangular prism shaped tent, you need to calculate the area of each face and add them all together.
First, calculate the area of the two triangular ends. Each end is a right triangle, so you can use the formula A = 0.5 * base * height. The base of each triangle is the width (20 ft.) and the height is the height of the prism (9 ft.).
A = 0.5 * 20 * 9 = 90 ft² for each end.
Next, calculate the area of the three rectangular sides. Two of the sides have heights of 9 ft. and lengths of 24 ft., while one has a height of 20 ft. (the hypotenuse of the triangular cover) and a length of 24 ft.
Total area of the three rectangular sides:
2 sides: 9 ft. * 24 ft. = 216 ft²
1 side: 20 ft. * 24 ft. = 480 ft²
Add the areas of the two ends and three sides together:
90 ft² (end 1) + 90 ft² (end 2) + 216 ft² + 480 ft² = 876 ft² + 696 ft² = 1572 ft²
Therefore, the surface area of the triangular prism shaped tent is 1,572 ft².