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
30,772 cm2
30,772 cm squared
17,550 cm2
17,550 cm squared
20,250 cm2
To find how many square centimeters of glass are needed for the coffee table, we need to find the surface area of the 6 rectangular glass sides shown in the 2-dimensional unfolded version of the hexagonal prism.
Each rectangular side has dimensions of 75 cm (height) by 38.97 cm (perpendicular height).
Surface Area of one rectangular side = Height x Perpendicular Height
Surface Area of one rectangular side = 75 cm x 38.97 cm
Surface Area of one rectangular side = 2927.75 cm2
Since there are 6 rectangular sides, we multiply the surface area of one side by 6:
Total Surface Area of all 6 glass sides = 2927.75 cm2 x 6 = 17,566.5 cm2
Therefore, the furniture company will need 17,550 cm2 of glass to make one coffee table.
The correct answer is:
17,550 cm2