Use the image to answer the 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.
(1 point)
Responses
40,500 cm2
40,500 cm squared
17,550 cm2
17,550 cm squared
20,250 cm2
20,250 cm squared
30,772 cm2
To find how many cm^2 of glass are needed for the coffee table, we need to calculate the lateral surface area of the hexagonal prism.
The lateral surface area can be calculated by determining the area of each vertical rectangle on the net and adding them up.
Each vertical rectangle has a height of 75 cm and a width equal to one side of the hexagon. The area of one rectangle can be found by multiplying 75 cm by the side length of 45 cm, which equals 3375 cm^2.
Since there are 6 vertical rectangles making up the lateral surface area, we need to multiply the area of one rectangle by 6 to get the total lateral surface area of the hexagonal prism.
3375 cm^2 * 6 = 20,250 cm^2
Therefore, the coffee table will require 20,250 cm^2 of glass.
The correct answer is 20,250 cm^2.