In a regular rectangular pyramid, the height is 6, the side edge is 8. Find its volume.

We will find the volume by the formula:
V = 1/3 * h * S.
Let’s designate this pyramid SABCD. By condition, the pyramid is correct at the base – a square. Find half of the diagonal, which is the leg in the right-angled triangle SOA, SO is the height of the pyramid.
AO = √ (SA² – SO²) = √ (64 – 36) = √28.
The whole diagonal of the square is 2√28.
Find the area of the base through the diagonals:
S = d² / 2 = 4 * 28/2 = 56.
We have all the necessary data, we find the volume of the pyramid:
V = 1/3 * h * S = 1/3 * 6 * 56 = 112.
Answer: 112.