Find the height of a regular quadrangular pyramid, the side of the base is 2 and the side edge is √11.

The height of a regular quadrangular pyramid is the leg of a right-angled triangle, the second leg of which is equal to 1/2 of the side of the base, and the hypotenuse is equal to the apothem of the pyramid.

Therefore, we need to find what the apothem of this pyramid is equal to.

The apothem of a regular quadrangular pyramid is a leg of a right-angled triangle, the hypotenuse of which is equal to the lateral rib, and the second leg is 1/2 side of the base of the pyramid.

Let’s use the Pythagorean theorem:

a² = (√11) ² – (2 * 1/2) ²,

a² = 11 – 1,

a = √10.

Now we can find the height of the pyramid:

h² = (√10) ² – (2 * 1/2) ²,

h² = 10 – 1,

h² = 9,

h = 3.

Answer: h = 3.