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
the length of one of the triangle sides 4.75
To determine the surface area of the tent, we first need to calculate the area of each face of the triangular prism.
1. The two triangular faces:
- Each triangular face is a right triangle with a base of 4.75 and a height of 4.
- To find the area of one triangular face, we can use the formula for the area of a triangle: 1/2 * base * height.
- Area of one triangular face = 1/2 * 4.75 * 4 = 9.5 square units.
- Since there are two triangular faces, the total area of the triangular faces is 2 * 9.5 = 19 square units.
2. The three rectangular faces:
- Each rectangular face has a length of 8 and a width of 5.
- To find the area of one rectangular face, we can use the formula for the area of a rectangle: length * width.
- Area of one rectangular face = 8 * 5 = 40 square units.
- Since there are three rectangular faces, the total area of the rectangular faces is 3 * 40 = 120 square units.
3. Total surface area of the tent:
- To find the total surface area of the tent, we can sum the areas of all the faces.
- Total surface area = triangular faces area + rectangular faces area
- Total surface area = 19 + 120 = 139 square units.
Therefore, you would need 139 square units of fabric to make the tent.