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 triangles: 40 mm
Height of the base triangle: 35 mm
Slant height of the equilateral triangular faces: 45 mm
(1 point)
3, 062.5 mm2
170, 000 mm2
153, 125 mm2
3, 400 mm2
The formula to calculate the surface area of a triangular pyramid is given by:
Surface Area = Base Area + 1/2 * Perimeter of Base * slant height
First, let's calculate the base area of the triangular pyramid. Since the base is an equilateral triangle, we can use the formula for the area of an equilateral triangle:
Base Area = sqrt(3)/4 * (side length)^2
Base Area = sqrt(3)/4 * (40 mm)^2 = 692.82 mm^2
Next, let's calculate the perimeter of the base triangle:
Perimeter of Base = 3 * side length = 3 * 40 mm = 120 mm
Now, we can calculate the surface area of one tea bag:
Surface Area = 692.82 mm^2 + 1/2 * 120 mm * 45 mm
Surface Area = 692.82 mm^2 + 5400 mm^2
Surface Area = 6092.82 mm^2
Since we need to make 50 tea bags, the total amount of nylon needed is:
Total Nylon = 6092.82 mm^2 * 50 = 304641 mm^2
Therefore, the amount of nylon needed to make 50 tea bags is approximately 304641 mm^2.
Answer: 3, 062.5 mm2