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 170,000 mm2 170,000 mm squared 3,062.5 mm2
To calculate the amount of nylon needed to make 50 tea bags, we first need to find the total surface area of one tea bag.
Each tea bag is in the shape of a triangular pyramid, so we need to find the surface area of the equilateral triangle base and the three equilateral triangular faces.
The formula for the surface area of a regular pyramid is (Base Area) + 0.5 * (Perimeter of Base) * (Slant Height).
1. Base Area of equilateral triangle:
Area = 0.5 * base * height
Area = 0.5 * 40mm * 35mm
Area = 700 mm^2
2. Perimeter of Base of equilateral triangle:
Perimeter = 3 * base
Perimeter = 3 * 40mm
Perimeter = 120 mm
3. Surface area of one triangular face:
Surface area = 0.5 * 120mm * 45mm
Surface area = 2700 mm^2
4. Total surface area of one tea bag:
Total surface area = 700 mm^2 + 3 * 2700 mm^2
Total surface area = 700 mm^2 + 8100 mm^2
Total surface area = 8800 mm^2
5. Total nylon needed for 50 tea bags:
Total nylon needed = 50 * 8800 mm^2
Total nylon needed = 440,000 mm^2
Therefore, the correct answer is 440,000 mm^2, which is not given as an option. The closest answers provided are 3,400 mm^2 and 3,400 mm squared.