A factory makes nylon tea bags the bags are in the shape of a triangular pyramid how much nylon is needed to make 50 tea bags given the following dimensions base of the equilateral triangle. 40 mm height of the base triangle 35 mm slant height of the equilateral triangle faces 45mm
To calculate the amount of nylon needed to make 50 tea bags in the shape of a triangular pyramid, we first need to calculate the total surface area of one tea bag and then multiply that by 50.
The total surface area of the triangular pyramid tea bag can be calculated using the formula:
Surface Area = Base Area + (1/2) x Perimeter of Base x Slant Height
First, let's calculate the base area of the equilateral triangle:
Base Area = (1/2) x Base x Height
Base Area = (1/2) x 40mm x 35mm
Base Area = 700 mm^2
Next, let's calculate the perimeter of the equilateral triangle:
Perimeter of Base = 3 x Base
Perimeter of Base = 3 x 40mm
Perimeter of Base = 120mm
Now, let's calculate the total surface area of one tea bag:
Surface Area = 700mm^2 + (1/2) x 120mm x 45mm
Surface Area = 700mm^2 + 5400mm^2
Surface Area = 6100mm^2
Finally, multiply the surface area of one tea bag by 50 to get the total amount of nylon needed to make 50 tea bags:
Total Nylon Needed = 6100mm^2 x 50
Total Nylon Needed = 305,000mm^2
Therefore, 305,000 square millimeters of nylon is needed to make 50 tea bags in the shape of a triangular pyramid with the given dimensions.