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
17,550 cm2
17,550 cm squared
40,500 cm2
40,500 cm squared
20,250 cm2
20,250 cm squared
30,772 cm2
30,772 cm squared
To find out how many cm2 of glass are needed, we need to calculate the total surface area of the hexagonal prism.
The formula for the surface area of a hexagonal prism is:
Surface Area = 2*(base area of hexagon) + (perimeter of hexagon)*(height)
From the illustration, we can see that the base area of the hexagon is 90 cm2.
The perimeter of the hexagon is 6*15 = 90 cm (as each side of the hexagon is 15 cm).
The height of the prism is 38.97 cm.
Using the formula:
Surface Area = 2*(90) + (90)*(38.97)
Surface Area = 180 + 3507.3
Surface Area = 3687.3 cm2
Since the glass sides are made up of the vertical rectangular sides connecting the hexagons, we need to calculate the surface area of these sides for one coffee table.
Each vertical rectangle has a base width of 75 cm and a height of 38.97 cm.
So, the surface area of one vertical rectangle is 75*38.97 = 2924.25 cm2.
There are 6 of these vertical rectangles on the hexagonal prism.
Therefore, the total surface area of the glass sides for one coffee table is 6*2924.25 = 17545.5 cm2.
Therefore, the closest answer is:
17,550 cm2