Question

An illustration shows a table in the shape of a 3-dimensional hexagonal prism, and its 2-dimensional unfolded version.

The 3-dimensional prism shows a hexagon tabletop and table bottom with six vertical rectangular sides connecting the six edges of each hexagon to the other, and also connected to each other. The unfolded version shows 6 vertical rectangles connected to one another horizontally with a vertical length of 75 centimeters. Two identical hexagons are adjoined to the top and bottom of the first vertical rectangle. The diagonal of the top hexagon, shown as a dotted line, is labeled as 90 centimeters. A side of the bottom hexagon is labeled as 45 centimeters, and the perpendicular height from the center of the hexagon to the middle of a side is labeled as 38.97 centimeters. The perpendicular height is denoted by a right angle symbol.
First Choice Interior makes a coffee table in the shape of a regular hexagonal prism. The top is made of wood, the sides of glass, and the bottom of metal. Use the net to find how many cm2 of glass are needed for the furniture company to make one coffee table.
30,772 cm2
20,250 cm2
17,550 cm2
40,500 cm2

Answer 1

[AI-generated answer — Bot GPT 3.5]

The total surface area of a hexagonal prism can be calculated by finding the sum of the areas of all the individual faces.

Since the top and bottom hexagons are identical, we can calculate the area of one hexagon and multiply by 2.

Area of one hexagon = (3√3/2) * side^2
Area of top and bottom hexagon = 2 * (3√3/2) * (90)^2 = 7029 cm^2

The lateral area of the prism can be calculated by finding the perimeter of the hexagon and multiplying by the height.

Perimeter of hexagon = 6 * side = 6 * 45 = 270 cm
Lateral area = perimeter * height = 270 * 75 = 20250 cm^2

Therefore, the total surface area of the hexagonal prism coffee table is:
7029 (top and bottom) + 20250 (sides) = 27279 cm^2

Since the sides are made of glass, the furniture company would need 20250 cm^2 of glass for each coffee table.

Therefore, the correct answer is 20,250 cm^2.