Given a regular quadrangular pyramid, the side of the base is 2 cm, and the side edge is 3 cm. Find the height.

1. It is known that the base of a regular quadrangular pyramid is a square.

Let’s denote the base ABCD, top S, height SO.

2. Point O lies at the intersection of the diagonals of the square, which are mutually perpendicular by the properties of the square, equal, the intersection point is divided in half.

So in triangle AOD leg AO is equal to leg OD.

By the Pythagorean theorem, we calculate the square of the leg AO.

2 AO ^ 2 = AD ^ 2 = 4.

AO ^ 2 = 2.

3. In the ASO triangle, find the OS leg.

OS ^ 2 = AS ^ 2 – AO ^ 2 = 3 ^ 2 – 2 = 9 – 2 = 7;

OS = 7 ^ 1/2 cm.

Answer: The height of the pyramid is 7 ^ 1/2 cm = 2.65 cm.

in which starts in the triangle AOD