In a regular quadrangular pyramid, the side edge is formed by the base plane at an angle of 45 °

In a regular quadrangular pyramid, the side edge is formed by the base plane at an angle of 45 °, the side of the pyramid base is 6 cm. find the volume of the pyramid.

Let’s find the height of the pyramid:

6 * sin (45) = 6 * √2 / 2 = 3 * √2.

1/2 base diagonal:

6 * cos (45) = 3 * √2.

Then the diagonal of the base is:

3 * √2 * 2 = 6 * √2.

Base side:

6 * √2 * √2 / 2 = 3.

The volume of the pyramid is easy to find by the formula V = 1/3 * h * S, where V is the volume, h is the height, S is the area of the base.

V = 1/3 * 3 * √2 * 3 ^ 3 = 9√2.