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)
A. 30,772 cm2
B. 17,550 cm2
C. 40,500 cm2
D. 20,250 cm2
To find the total surface area of the glass used for the coffee table, we need to calculate the area of the six rectangular glass sides.
The net of a regular hexagonal prism consists of six rectangles: three pairs of congruent rectangles. The dimensions of each rectangle can be calculated based on the dimensions of the hexagonal prism.
Given that the regular hexagonal prism has a side length of 30 cm (since the top of the coffee table is a regular hexagon), we can calculate the dimensions of each rectangle:
Each pair of congruent rectangles will have dimensions:
- Length: 30 cm
- Width: the height of the prism, which can be calculated using the Pythagorean theorem:
Height = √(30^2 - (30/2)^2) = √(900 - 225) = √675 ≈ 26.01 cm
The total surface area of the glass is the sum of the areas of the six rectangles:
2(30 * 26.01) * 3 = 30.02 * 6 = 180.14 cm2.
Therefore, Option B is correct: 17,550 cm2.