In a regular quadrangular pyramid, the side surface is 14.76 cm2, and the total surface

In a regular quadrangular pyramid, the side surface is 14.76 cm2, and the total surface is 18 cm2. Determine the volume of the pyramid.

Determine the area of the base of the pyramid.

Sb = Sпов – Sbok = 18 – 14.76 = 3.24 cm2.

Then the side of the base is: AB = BC = CD = AD = √3.24 = 1.8 cm.

Determine the area of the triangle MCD. Smsd = S side / 4 = 14.76 / 4 = 3.69 cm2.

Smsd = CD * MН / 2.

MH = 2 * Smsd / CD = 2 * 3.69 / 1.8 = 4.1 cm.

Segment OH = AD / 2 = 1.8 / 2 = 0.9 cm.

In the right-angled triangle MOН, we define the leg MO.

MO ^ 2 = MH ^ 2 – OH ^ 2 = 16.81 – 0.81 = 16.

MO = 4 cm.

Then V = Sbn * MO / 3 = 3.24 * 4/3 = 4.32 cm3.

Answer: The volume of the pyramid is 4.32 cm3.