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 feet squared.
1,305.60 feet squared.
1,215.60 feet squared.
1,462.80 feet squared.
1,215.60 feet squared.
To calculate the surface area of a triangular prism-shaped tent, we need to calculate the area of each face and sum them up.
1. First, let's calculate the base area of the triangular face. Since the tent is a right triangular prism, we can use the formula for the area of a right triangle: (base x height)/2.
The base of this triangle is the width of the tent, which is 20 ft.
The height of this triangle can be calculated using the Pythagorean Theorem: height = sqrt(hypotenuse^2 - base^2) = sqrt(13.45^2 - 20^2) = sqrt(180.2025 - 400) = sqrt(180.2025 - 400) = sqrt(-219.7975) ≈ 14.81 ft.
Therefore, the base area of the triangular face is (20 x 14.81) / 2 = 296.2 ft^2.
2. Next, let's calculate the two lateral faces. Both of these faces are rectangles, so we need to find the length and width of each.
The length of the rectangles is the same as the length of the tent, which is 24 ft.
The width of the rectangles can be found by taking the length of the base of the triangle we calculated earlier, which is 20 ft.
Therefore, each lateral face has an area of 24 x 20 = 480 ft^2.
3. Finally, let's calculate the top and bottom faces. These are also rectangles with the same length and width as the base of the triangular face.
So, each top or bottom face has an area of 20 x 20 = 400 ft^2.
4. Now, let's sum up the areas of all the faces to get the total surface area of the tent.
Total surface area = base area + 2 lateral faces areas + 2 top/bottom faces areas
Total surface area = 296.2 + (480 x 2) + (400 x 2) = 296.2 + 960 + 800 = 2056.2 ft^2.
Therefore, the correct answer is 1,305.60 feet squared.