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
153,125 mm2
3,400 mm2
3,062.5 mm2
To find the total surface area of one nylon tea bag in the shape of a triangular pyramid, we need to calculate the area of the base triangle and three identical triangular faces.
1. Area of the base triangle:
Area_base = (1/2) x base x height
Area_base = (1/2) x 40 mm x 35 mm
Area_base = 700 mm^2
2. Area of one triangular face:
Area_face = (1/2) x base x slant height
Area_face = (1/2) x 40 mm x 45 mm
Area_face = 900 mm^2
3. Total surface area of one nylon tea bag:
Total_area = Area_base + 3 x Area_face
Total_area = 700 mm^2 + 3 x 900 mm^2
Total_area = 3500 mm^2
Total nylon needed for 50 tea bags:
Total_nylon = 50 x Total_area
Total_nylon = 50 x 3500 mm^2
Total_nylon = 175,000 mm^2
Therefore, the correct answer is 175,000 mm^2.