# hexagonal pyramid height

• Feb 17th 2010, 05:09 AM
Mukilab
hexagonal pyramid height
I need to calculate the height of a hexagonal pyramid given the base length sides as 2cm and the slant edges as 6cm from each vertex.

The formula?
• Feb 17th 2010, 05:55 AM
davesymm
Quote:

Originally Posted by Mukilab
I need to calculate the height of a hexagonal pyramid given the base length sides as 2cm and the slant edges as 6cm from each vertex.

The formula?

If I understand your question correctly then you have a six sided pyramid (with a regular hexagonal base) with side lengths 2cm and corner to top-point length 6cm?

If so, a regular hexagon is made up of six regular (equilateral) triangles, so you know the distance from a corner to the centre of the hexagon is also 2cm. If you take a cross section of the pyramid across two opposite corners you will have a 2d triangle of which you know the length of the base and hypotenuse. You should be able to work out the height using standard trig from here :)
• Feb 17th 2010, 08:52 AM
Diagonal
The [regular] hexagon consists of six equilateral triangles, all sides of length 2 cm. A diagonal of the hexagon then has length 4. If you drop a perpendicular to the center, you'll have a right triangle with hypotenuse 6, and one side 2. The other side, the altitude or height, can be found using Pythagoras.