Question

90 cm 75 cm 38.97 cm 45 cm

First choice interior makes a coffee table in the shape of a regular hexagon prism the top is made of wood and the sides of glass and the bottom of metal used the net to find how many cm of glasses is needed for furniture the company to make one coffee table

40, 500 cm
30, 772 cm
20,250 cm
17, 550 cm

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find out how much glass is needed for one coffee table, we need to calculate the surface area of all the faces of the hexagon prism except for the top (which is made of wood).

The hexagon prism has 6 rectangular faces and 2 hexagonal faces. The dimensions of the rectangular faces are as follows:
- Length: 45 cm
- Width: 90 cm

The dimensions of the hexagonal faces are as follows:
- Side length of the hexagon: 45 cm
- Apothem (distance from the center of the hexagon to the midpoint of a side): 38.97 cm

Now, we calculate the surface area of all the glass sides of the prism by adding up the areas of all the faces:

6 rectangular faces:
Surface area = 6 * (length * width)
Surface area = 6 * (45 cm * 90 cm)
Surface area = 6 * 4050 cm^2
Surface area = 24300 cm^2

2 hexagonal faces:
Surface area = 2 * (1/2 * Perimeter of hexagon * Apothem)
Surface area = 2 * (1/2 * (6 * 45 cm) * 38.97 cm)
Surface area = 2 * (135 cm * 38.97 cm)
Surface area = 2 * 5251.95 cm^2
Surface area = 10503.9 cm^2

Total glass surface area = 24300 cm^2 + 10503.9 cm^2
Total glass surface area = 34803.9 cm^2

Therefore, the furniture company needs 34,803.9 cm^2 of glass to make one coffee table. None of the provided options match this calculation exactly, but the closest option is 30,772 cm.