The base area of a regular quadrangular pyramid is 36cm ^ 2, the side edge is 5cm.

The base area of a regular quadrangular pyramid is 36cm ^ 2, the side edge is 5cm. Find the apothem and the side surface area of the pyramid.

Since the pyramid is correct, there is a square at its base. The area of the base, by condition, is 36 cm2, then the side of the base is: AB = BC = CD = AD = √ 36 = 6 cm.

Let’s draw the apothem OH and from the right-angled triangle OO1H, by the Pythagorean theorem we will determine its length.

OH ^ 2 = OA ^ 2 – AH ^ 2 = 52 – 32 = 25 – 9 = 16.

OH = √16 = 4 cm.

The area of the lateral surface of the pyramid is equal to the four areas of the isosceles triangles AOD.

Side = 4 * AD * OH / 2 = 4 * 6 * 4/2 = 48 cm2.