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 40,500 cm2 40,500 cm squared 20,250 cm2
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To find the total surface area of the regular hexagonal prism coffee table, we need to calculate the area of each individual shape and then add them together.
The net of a regular hexagonal prism consists of 2 hexagons and 6 rectangles.
The formula for the area of a hexagon is (3√3 * s^2)/2, where s is the length of one side of the hexagon.
Given that the side length of the hexagon is the same as the side length of the prism, we can calculate the area of one hexagon:
(3√3 * 50^2)/2 = (3√3 * 2500)/2 = (7500√3)/2 = 3750√3 ≈ 6495.5 cm^2
Since there are 2 hexagons, the total area of the hexagons is 2 * 6495.5 = 12991 cm^2
The formula for the area of a rectangle is l * w, where l is the length and w is the width.
Given that the length of the rectangle is equal to the perimeter of the hexagon (6 * 50 = 300 cm) and the width is equal to the height of the prism (100 cm), we can calculate the area of one rectangle:
300 * 100 = 30000 cm^2
Since there are 6 rectangles, the total area of the rectangles is 6 * 30000 = 180000 cm^2
Now, we can calculate the total surface area of the regular hexagonal prism coffee table by adding the areas of the hexagons and rectangles together:
12991 + 180000 = 192991 cm^2
Therefore, the furniture company would need 192991 cm^2 of glass to make one coffee table.