A Christmas decoration is in the shape of a square based pyramid. All edges in the pyramid have a measurement of 4cm how do you find the height of the pyramid?

1 Answer
Oct 24, 2015

Answer:

Calculate the height of an equilateral triangle with sides all #4cm#, then an isosceles triangle with two sides of that length and a #4cm# base.

Explanation:

A triangular face of the pyramid is equilateral, so divides into two right angled triangles with sides #4cm#, #2cm# and #2sqrt(3)cm#.

Then looked at from one side, the pyramid looks like a isosceles triangle with base #4cm# and sides #2sqrt(3)cm#. This divides into two right angled triangles with sides #2sqrt(3)cm#, #2cm# and #2sqrt(2)cm#, this last length being the height of the pyramid.

Alternatively, note that stacking two of these pyramids back to back will result in a regular octohedron, who diagonal measurement is the diagonal of a square with sides of length #4cm#, i.e. #4sqrt(2)cm#. Then the height of the pyramid is half this, i.e. #2sqrt(2)cm#.