Question

What is the slant height in a rectangular or square pyramid?(1 point) Responses the height from the apex straight down to the base of the triangular face where it forms a right angle the height from the apex straight down to the base of the triangular face where it forms a right angle an edge of a triangular face an edge of a triangular face the distance across the triangular face the distance across the triangular face the height of the pyramid from the apex straight down to the middle of the base of the pyramid the height of the pyramid from the apex straight down to the middle of the base of the pyramid

Answer 1

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 153,125 mm2 153,125 mm squared 3,400 mm2 3,400 mm squared 3,062.5 mm2 3,062.5 mm squared

Answer 2

the height from the apex straight down to the base of the triangular face where it forms a right angle

Answer 3

The total surface area of a triangular pyramid can be calculated by finding the area of the base triangle and adding the areas of the three triangular faces.

Area of the base triangle = sqrt(3)/4 * side^2
= sqrt(3)/4 * 40^2
= sqrt(3)/4 * 1600
= 400sqrt(3) mm^2

Area of one triangular face = 1/2 * base * height
= 1/2 * 40 * 45
= 900 mm^2

Total surface area of one tea bag = 400sqrt(3) + 3(900)

Total surface area of 50 tea bags = 50 * (400sqrt(3) + 3(900))
= 50(400sqrt(3) + 2700)
≈ 170,000 mm^2

Therefore, 170,000 mm^2 of nylon is needed to make 50 tea bags.

Answer: 170,000 mm squared