The tent below is shaped like a triangular prism. EXPLAIN how you would determine the surface area of the tent to find the amount of fabric needed to make the tent. Remember to describe each face of the triangular prism.
The tent: (4.75ft) (4 ft) (5 ft) (8ft)
To find the surface area of the tent, we need to calculate the area of each face of the triangular prism and then add them all together.
1. Base: The base of the triangular prism is a triangle with base 4.75 ft and height 4 ft. The area of the base can be calculated using the formula for the area of a triangle: 1/2 * base * height. Therefore, the area of the base is 1/2 * 4.75 ft * 4 ft = 9.5 sq ft.
2. Sides: The triangular prism has three sides that are rectangles with dimensions 4.75 ft (base) by 5 ft (height). The area of each side can be calculated by multiplying the base by the height. Therefore, the area of each side is 4.75 ft * 5 ft = 23.75 sq ft. Since there are three sides, the total area for all three sides is 3 * 23.75 sq ft = 71.25 sq ft.
3. Top and bottom: The top and bottom faces of the triangular prism are each rectangles with dimensions 4 ft by 4.75 ft. The area of each top/bottom face can be calculated by multiplying the length by the width. Therefore, the area of each top/bottom face is 4 ft * 4.75 ft = 19 sq ft. Since there are two top/bottom faces, the total area for both top/bottom faces is 2 * 19 sq ft = 38 sq ft.
Now, to find the total surface area of the tent, add up the areas of all the faces:
Base + Sides + Top/Bottom = 9.5 sq ft + 71.25 sq ft + 38 sq ft = 118.75 sq ft
Therefore, the amount of fabric needed to make the tent is 118.75 square feet.