The lateral surface area of a regular quadrangular prism is 48 cm2. Find the volume of this prism

The lateral surface area of a regular quadrangular prism is 48 cm2. Find the volume of this prism if its lateral edge is 4 cm.

At the base of a regular quadrangular prism lies a square, the lateral faces of the prism are equal to each other quadrangles, therefore, the area of each of them is equal to a quarter of the area of the lateral surface:

Sgr = Sside / 4 = 48/4 = 12 cm2.

On the other hand, the area of each side face is equal to the product of the side of the base and the side edge:

Sgr = h * a.

Hence,

a = Sgr / h = 12/4 = 3 cm – side of the base.

Base area:

Sb = a ^ 2 = 3 ^ 2 = 9 cm2.

The volume of the prism is equal to the product of the area of the base and the length of the lateral rib:

V = Sbn * h = 9 * 4 = 36 cm3.