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
George C.
Oct 24, 2015

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.

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