In a regular quadrangular pyramid, all edges are equal to 1. Find the height of the pyramid.

In a regular quadrangular pyramid at the base there is also a regular quadrilateral, that is, a square with a side equal to 1 and a diagonal equal to:
√ [(1) ^ 2 + (1) ^ 2] = √ 2. (From the Pythagorean theorem).

In the section of the pyramid, passing through the height H of the pyramid, there is an isosceles triangle with sides 1 and 1, the base of the triangle is the diagonal of the square, equal to √ 2, the height is N.

Let’s find the height of the pyramid H according to the Pythagorean theorem:
H ^ 2 = 1 ^ 2 – [(√ 2) / 2] ^ 2 = 1 – 2/4 = 1/2.
H = √ (1/2) = √ 2/2.