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
30,772 cm2
30,772 cm squared
17,550 cm2
17,550 cm squared
20,250 cm2
20,250 cm squared
40,500 cm2
40,500 cm squared
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To find how many cm2 of glass are needed for the coffee table, we need to find the total surface area of the six vertical rectangles in the unfolded version of the table. Each rectangle has a width of 45 cm and a height of 75 cm (given in the illustration).
The formula to calculate the surface area of a rectangle is:
Surface area = width x height
Surface area of one rectangle = 45 cm x 75 cm = 3375 cm2
Since there are six identical rectangles, we need to multiply the surface area of one rectangle by 6 to get the total surface area of glass needed for the coffee table.
Total surface area of glass = 3375 cm2 x 6 = 20,250 cm2
Therefore, the correct answer is:
20,250 cm2