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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
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

1 answer

To determine how many square centimeters of glass are needed for the sides of the regular hexagonal prism coffee table, we need to calculate the area of the six rectangular sides given the provided dimensions.

  1. Identifying dimensions:

    • The height of the table (vertical length of the rectangles) is given as 75 cm.
    • The side length of each hexagon is given as 45 cm.

  2. Calculating the area of one rectangular side: The area \( A \) of one rectangular side can be calculated using the formula: \[ A = \text{height} \times \text{width} \] The width of each rectangle is equal to the side length of the hexagon: \[ A = 75 , \text{cm} \times 45 , \text{cm} = 3375 , \text{cm}^2 \]

  3. Calculating the total area for all six rectangular sides: Since there are six sides: \[ \text{Total area} = 6 \times 3375 , \text{cm}^2 = 20250 , \text{cm}^2 \]

Thus, the amount of glass needed to make one coffee table is 20,250 cm².

Therefore, the correct answer is:

20,250 cm²