A factory makes nylon tea bags. The bags are the shape of a triangular pyramid. How much nylon is needed to make 50 tea bags?
Base of equilateral triangles 40
Height of base triangle 35
Slant height of equilateral triangular faces 45
To find the surface area of one triangular pyramid tea bag, we first need to find the area of the equilateral triangle base:
Area of equilateral triangle = (sqrt(3) / 4) * (side)^2
Area = (sqrt(3) / 4) * 40^2
Area = (sqrt(3) / 4) * 1600
Area = 347.70 sq. units
Next, we need to find the area of the 3 triangular faces:
Area of triangular face = (1/2) * base * height
Area = (1/2) * 40 * 35 = 700 sq. units
Now, we can calculate the total surface area of one tea bag:
Total surface area = (3 * area of triangular face) + area of base
Total surface area = (3 * 700) + 347.70
Total surface area = 2100 + 347.70
Total surface area = 2447.70 sq. units
Since we are making 50 tea bags, the total nylon needed for all 50 tea bags would be:
Total nylon needed = 2447.70 sq. units * 50
Total nylon needed = 122,385 sq. units
Therefore, 122,385 sq. units of nylon is needed to make 50 tea bags.