Lateral Surface Area Quick Check
2 of 52 of 5 Items
Question
Use 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
30,772 cm2
30,772 cm squared
20,250 cm2
To find the lateral surface area of the regular hexagonal prism coffee table, we need to calculate the area of the 6 vertical rectangular sides.
Each of the 6 vertical rectangles has a length of 75 cm and a height equal to the perpendicular height from the center of the hexagon to the middle of a side, which is 38.97 cm.
Therefore, the lateral surface area of one vertical rectangle is 75 cm * 38.97 cm = 2924.25 cm^2.
Since there are 6 vertical rectangles, the total lateral surface area of the regular hexagonal prism coffee table is 6 * 2924.25 cm^2 = 17545.5 cm^2.
Therefore, the correct answer is:
17,545 cm^2