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
170,000 mm2
170,000 mm squared
3,062.5 mm2
3,062.5 mm squared
3,400 mm2
3,400 mm squared
153,125 mm2
153,125 mm squared
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To find the total surface area of one triangular pyramid tea bag, we need to calculate the area of the three equilateral triangles that make up the sides and the base of the pyramid.
Area of each equilateral triangle = (1/2) * base * height
Area of each triangular face = (1/2) * 40 mm * 35 mm = 700 mm²
Next, we calculate the area of the base triangle:
Area of the base triangle = (1/2) * base * height
Area of the base triangle = (1/2) * 40 mm * 35 mm = 700 mm²
Now, we calculate the lateral area of the triangular pyramid (the three triangular faces):
Lateral area = 3 * 700 mm² = 2,100 mm²
The total surface area of one tea bag is the sum of the lateral area and the base triangle area:
Total surface area of one tea bag = 2,100 mm² + 700 mm² = 2,800 mm²
To calculate the total surface area of 50 tea bags, we multiply the surface area of one tea bag by 50:
Total surface area of 50 tea bags = 2,800 mm² * 50 = 140,000 mm²
Therefore, the factory would need 140,000 mm² of nylon to make 50 tea bags.