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.
length 8
with 5
height 4
To determine the surface area of the tent, we need to calculate the area of each face of the triangular prism and then sum them up.
1. Identify the faces of the triangular prism:
- Base: The base of the triangular prism is a triangle with a base of 8 units and a height of 4 units. The area of this triangle can be calculated using the formula:
Area = 1/2 * base * height
Substitute the values:
Area = 1/2 * 8 * 4 = 16 square units
- Side faces: The triangular prism has 3 identical rectangular faces that are 8 units by 5 units each. The area of each rectangular face can be calculated as:
Area = length * width
Substitute the values:
Area = 8 * 5 = 40 square units
Since there are 3 identical faces, the total area for all side faces will be: 3 * 40 = 120 square units
2. Calculate the total surface area by summing up the areas of all faces:
Total surface area = Base area + Total side face area
Total surface area = 16 + 120 = 136 square units
Therefore, to find the amount of fabric needed to make the tent, we would need 136 square units of fabric.