SOLUTION: Thank you in advance for help:) A jewelry box has the shape of a prism with a regular hexagonal base of 196.65. The sides of the hexagonal base are ALL 8.70 inches. If the height

Algebra ->  Surface-area -> SOLUTION: Thank you in advance for help:) A jewelry box has the shape of a prism with a regular hexagonal base of 196.65. The sides of the hexagonal base are ALL 8.70 inches. If the height       Log On


   

Question 1117015: Thank you in advance for help:)
A jewelry box has the shape of a prism with a regular hexagonal base of 196.65. The sides of the hexagonal base are ALL 8.70 inches. If the height of the box is 16.07in, what would the surface area be of the wood used to make the jewelry box?
Options:
1237.79
1232.15
1242.93
1223.47
None of the above
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the hexagonal base has an area of 165.65 square inches.

the formula for the area of the hexagonal base is 3 * sqrt(3) / 2 * s^2, where s is the side of the hexagon.

the length of a side of the hexagon is 8.7 inches.

3 * sqrt(3) / 2 * 8.7^2 = 196.6483884 which rounds to 196.65.

the height of the hexagonal prism is 16.07 inches.

the hexagonal prism has 6 vertical sides.

the area of each of the sides is equal to 16.07 * 8.7 = 139.809.

6 * that is equal to 838.854.

add the area of the top and bottom base and you get 838.854 + 2 * 196.65 = 1232.154 square inches.

that rounds to 1232.15 square inches which is your second selection down from the top.

the total surface area includes all 6 size plus the bottom and the top or the jewelry box.