Question
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? Good luck! 😘
The base of the equilateral triangles: 40 mm
Height of the base triangle: 35 mm
The slant height of the equilateral triangular faces: 45 mm
(1 point)
Responses
3,062.5 mm2
3,062.5 mm squared
170,000 mm2
170,000 mm squared
3,400 mm2
3,400 mm squared
153,125 mm2
To calculate the total surface area of one triangular pyramid tea bag, we need to find the area of the base triangle, the three faces, and the bottom.
1. Area of the base triangle:
Area = 1/2 * base * height
Area = 1/2 * 40 mm * 35 mm
Area = 700 mm²
2. Area of each triangular face:
Area = 1/2 * base * height
Area = 1/2 * 40 mm * 45 mm
Area = 900 mm²
3. Bottom area (base of the pyramid):
Area = 40 mm * 40 mm = 1600 mm²
4. Total surface area of one tea bag:
700 mm² (base) + 3 * 900 mm² (triangular faces) + 1600 mm² (bottom) = 4,300 mm²
5. Total nylon needed for 50 tea bags:
4,300 mm² * 50 = 215,000 mm²
Therefore, the correct answer is 215,000 mm².