SOLUTION: To the nearest tenth find the volume of a regular hexagonal pyramid with base edges of 12cm long and height of 15cm

Question 1659: To the nearest tenth find the volume of a regular hexagonal pyramid with base edges of 12cm long and height of 15cm
Answer by AnlytcPhil(1277) (Show Source):
You can put this solution on YOUR website!
To the nearest tenth find the volume of a regular hexagonal pyramid with base
edges of 12cm long and height of 15cm
`
Volume of a pyramid = Area of the base * Height * 1/3
`
So we begin by finding the area of the base.
The base is a regular hexagon. A regular hexagon is 6 congruent
equilateral triangles placed together like 6 pieces of pie:
`__
/\/\
\/\/
`
The area of one equilateral triangle is given by A = bh/2. The base
is the edge and the height is found by the Pythagorean theorem
`
` `/|\
12/h| \12
`/_`|`_\
` 6 ` 6
`
6² + h² = 12²
36 + h² = 144
` ` `h² = 144 - 36
` ` `h² = 108
` ` ` =
`
So the area of one equilateral triangle with edge 12 is
`
=
`
The area of the regular hexagon base of the pyramid is then
6 times this, or
`
Now since
`
Volume of a pyramid = Area of the base * Height * 1/3, we have
`
Volume = or,
`
Edwin J