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
The net of a regular hexagonal prism consists of 6 rectangles and 6 regular hexagons.
The formula for the surface area of a regular hexagonal prism is:
Surface Area = 6(area of the hexagon) + 6(area of the rectangle)
Given that the top and bottom of the prism are hexagons, and the sides are rectangles, the total surface area would be the sum of 6 hexagons and 6 rectangles.
The formula for the surface area of a regular hexagon is:
Area = 3√3 * side^2
Given that the side length of the hexagon is the same as the side length of the prism:
Area = 3√3 * side^2 = 3√3 * side^2
The formula for the surface area of a rectangle is:
Area = length * width
Given that the rectangles have a specific length and width:
Area = 2 * length * width
The sum of the hexagons' area is: 6 * (3√3 * side^2) = 18√3 * side^2
The sum of the rectangles' area is: 6 * (2 * length * width) = 12 * length * width
The total surface area is: 18√3 * side^2 + 12 * length * width
Since the dimensions of the hexagonal prism are not provided in the question, we cannot calculate the exact area needed for the glass. Therefore, none of the provided answer choices can be confirmed as correct without additional information.