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
40,500 cm2
40,500 cm squared
20,250 cm2
20,250 cm squared
17,550 cm2
17,550 cm squared
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To find how many square centimeters of glass are needed for the coffee table, we need to calculate the surface area of the vertical rectangular sides.
From the unfolded version of the net of the hexagonal prism, we can see that each vertical rectangle has a length of 75 cm. The height of the vertical rectangles can be found by calculating the distance from the center of the hexagon to the middle of a side. This distance is given as 38.97 cm.
The total surface area of glass needed for one coffee table can be calculated by finding the combined area of all 6 vertical rectangles.
Area of one vertical rectangle = length x height
Area of one vertical rectangle = 75 cm x 38.97 cm
Area of one vertical rectangle = 2922.75 cm2
Total area of glass needed for all 6 vertical rectangles = 6 x 2922.75 cm2
Total area of glass needed = 17536.5 cm2
Therefore, 17,550 cm2 of glass are needed for the furniture company to make one coffee table.
So the answer is:
17,550 cm2
17,550 cm squared