The base of the pyramid is a rectangle with sides 5 and 8 cm.

The base of the pyramid is a rectangle with sides 5 and 8 cm. The length of each side edge of the pyramid is 12cm. Find the volume of the pyramid.

Let’s find out what the diagonal in the rectangle will be, which, according to the problem statement, serves as the base of the pyramid:

√ (5 ^ 2 + 8 ^ 2) = √89.

As you know, the height in such a pyramid will drop to the point of intersection of the diagonals, that is, half of the diagonal will be the leg of the triangle formed with the lateral edge.

Then the height can be calculated as follows:

√ (122 – (√89 / 2) 2) = √121.75.

Let’s determine what the volume of the pyramid will equal, for which we use the well-known formula:

V = Sosn * h: 3;

5 * 8 * √121.75: 3 = 40√121.75 / 3.

Answer: 40√121.75 / 3 cm3.