A factory makes nylon teabags. The bags are the shape of a triangular pyramid how much nylon is needed to make 50 teabags given the following dimensions.
Base of the equilateral triangle 40mm
Height of the base triangle: 35mm
Slant Heights of the equilateral triangle faces:45mm
To find the amount of nylon needed to make one triangular pyramid teabag, we first need to find the surface area of the equilateral triangle base.
The formula for the area of an equilateral triangle can be calculated as:
Area = (sqrt(3) / 4) * (side length)^2
Given that the base length of the equilateral triangle is 40mm, the area of the triangle base is:
Area = (sqrt(3) / 4) * (40mm)^2
Area = (sqrt(3) / 4) * 1600mm^2
Area = 800√3 mm^2
Next, we need to find the area of one triangular face of the pyramid. This can be calculated as:
Area = (1/2) * base * height
Area = (1/2) * 40mm * 35mm
Area = 700mm^2
Now, we can find the total surface area of the triangular pyramid by adding the areas of the four triangular faces:
Total Surface Area = 4 * 700mm^2
Total Surface Area = 2800mm^2
Since nylon fabric is needed for all 4 triangular faces of the pyramid, we would need 2800mm^2 of nylon fabric to make 1 teabag.
To make 50 teabags, the total amount of nylon needed would be:
Total Nylon = 2800mm^2 * 50
Total Nylon = 140,000mm^2
Therefore, 140,000mm^2 of nylon would be needed to make 50 triangular pyramid teabags.