Sara is making a model tent. How much material will she need? Explain the process to solve and show all calculations.
aka a triangle prism w=4 l=15 and h=3
To find the amount of material Sara will need, we first need to calculate the surface area of the tent, which is the total amount of material needed to cover the entire structure.
The surface area of a triangular prism can be calculated by finding the area of the three faces and adding them together.
1. Calculate the surface area of the two triangular faces:
The formula for the area of a triangle is:
Area = 1/2 * base * height
For a triangular prism, the triangle has a base equal to the width of the tent (4 units) and a height equal to the height of the tent (3 units).
Area of one triangular face = 1/2 * 4 * 3 = 6 square units
Since there are two triangular faces on the tent, the total area of both faces is:
Total area of triangular faces = 2 * 6 = 12 square units
2. Calculate the surface area of the rectangular face:
The formula for the area of a rectangle is:
Area = length * width
For a triangular prism, the rectangle has a width of 4 units equal to the width of the tent and a length equal to the length of the tent (15 units).
Area of the rectangular face = 15 * 4 = 60 square units
3. Calculate the total surface area of the tent:
Total surface area = Total area of triangular faces + Area of rectangular face
Total surface area = 12 + 60 = 72 square units
Therefore, Sara will need 72 square units of material to make the tent.
you shure
I apologize for the mistake in my previous response. Let's recalculate the surface area of the triangular prism correctly.
The formula for the surface area of a triangular prism is 2 * (area of base) + (perimeter of base) * height.
1. Area of the triangular base:
Area = 1/2 * base * height
Area = 1/2 * 4 * 3
Area = 6 square units
2. Perimeter of the base:
Perimeter = sum of all sides of the base
Perimeter = 4 + 4 + 15
Perimeter = 23 units
3. Surface area of the triangular prism:
Surface area = 2 * (6) + (23) * 3
Surface area = 12 + 69
Surface area = 81 square units
Therefore, Sara will need 81 square units of material to make the tent.