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. 4ft 5ft 8ft 4.75ft
To determine the surface area of the tent, we need to calculate the areas of each face of the triangular prism and then add them up.
1. The two triangle faces:
- Each of the triangle faces is an equilateral triangle with side lengths of 4 feet. To calculate the area of one triangle, we can use the formula:
Area = (1/4) * sqrt(3) * side length^2.
Area = (1/4) * sqrt(3) * 4^2 = (1/4) * sqrt(3) * 16 = 4sqrt(3) square feet.
Since there are two identical triangle faces, the total area for both would be 2 * 4sqrt(3) = 8sqrt(3) square feet.
2. The three rectangular faces:
- Each rectangular face has dimensions of 4.75 ft by 5 ft. To calculate the area of one rectangular face, we multiply the length by the width:
Area = length * width = 4.75 * 5 = 23.75 square feet.
Since there are three rectangular faces, the total area for all three would be 3 * 23.75 = 71.25 square feet.
Total surface area of the triangular prism tent:
8sqrt(3) + 71.25 = approximately 83.73 square feet
Therefore, approximately 83.73 square feet of fabric would be needed to make the tent.