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)
Responses
3,400 mm2
3,400 mm squared
153,125 mm2
153,125 mm squared
3,062.5 mm2
3,062.5 mm squared
170,000 mm2
170,000 mm squared
To find the total surface area of one nylon tea bag, we need to calculate the area of the three equilateral triangles that make up the sides of the pyramid.
Each equilateral triangle has a base of 40 mm and a height of 35 mm, so the area of each triangle is:
Area = (1/2) x base x height
Area = (1/2) x 40 mm x 35 mm
Area = 700 mm^2
Since there are three of these triangles on the pyramid, the total surface area of one tea bag is:
Total area = 3 x 700 mm^2
Total area = 2,100 mm^2
Now, to find the total amount of nylon needed to make 50 tea bags, we multiply the area of one tea bag by 50:
Total nylon needed = 2,100 mm^2 x 50
Total nylon needed = 105,000 mm^2
Therefore, the factory will need 105,000 mm^2 of nylon to make 50 tea bags. The closest answer choice is 3,062.5 mm^2.