- 06 Apr '07 18:53

Hexagonal prism:*Originally posted by wittywonka***What is the volume of a right hexagonal prism with each base's perimeter measuring 60 cm and with a height of 5 cm? What about a right octagonal prism with the same measurements?**

hexagon side = 10cm.

hexagon area = 6*10*sqrt(3)/4 = 15*sqrt(3) (6 times the area of an equilateral triangle with side length 10)

Volume = base*height = 15*sqrt(3)*5 = 75*sqrt(3).

The octogonal prism can be dealt with in the same way, though the calculations for the area of the base are a little messier. - 06 Apr '07 19:26

Why did you divide by four? I think you only divide by two...*Originally posted by GregM***Hexagonal prism:**

hexagon side = 10cm.

hexagon area = 6*10*sqrt(3)/4 = 15*sqrt(3) (6 times the area of an equilateral triangle with side length 10)

Volume = base*height = 15*sqrt(3)*5 = 75*sqrt(3).

The octogonal prism can be dealt with in the same way, though the calculations for the area of the base are a little messier. - 06 Apr '07 21:05No, but I did miss a square: the area of an equilateral triangle with side length S is S^2*sqrt(3)/4, so the correct numbers would be

hexagon area = 6*10^2*sqrt(3)/4 = 150*sqrt(3) (6 times the area of an equilateral triangle with side length 10)

Volume = base*height = 150*sqrt(3)*5 = 750*sqrt(3). - 07 Apr '07 01:06 / 1 edit

Where do you get sqrt(3) from? The area of the triangle is 25*sqrt(2).*Originally posted by GregM***No, but I did miss a square: the area of an equilateral triangle with side length S is S^2*sqrt(3)/4, so the correct numbers would be**

hexagon area = 6*10^2*sqrt(3)/4 = 150*sqrt(3) (6 times the area of an equilateral triangle with side length 10)

Volume = base*height = 150*sqrt(3)*5 = 750*sqrt(3).

Edit: Posted before checking - I'm thinking of sin(45)