If in a regular quadrangular pyramid the height is 4, and the area of the diagonal section is 6, then its volume is..

The diagonal section of the pyramid is an isosceles triangle APC, in which AP = CP.

Knowing the area of the diagonal section and the height of the pyramid, we determine the base of the triangle APC.

Ssech = AC * OP / 2.

AC = 2 * Ssection / OР = 6 * 2/4 = 3 cm.

At the base of the pyramid lies the square of AВСD, then Sbasn = D ^ 2/2 = AC ^ 2/2 = 9/2 = 4.5 cm2.

Let’s define the volume of the pyramid.

V = Sbn * OР / 3 = 4.5 * 4/3 = 6 cm3.

Answer: The volume of the pyramid is 6 cm3.