In a regular quadrangular pyramid, the side of the base is 12 cm, and the apothem of the side face is 8 cm.

univerkov | March 10, 2021 | education

In a regular quadrangular pyramid, the side of the base is 12 cm, and the apothem of the side face is 8 cm. Find the total surface area of the pyramid.

Determine the area of the base of the pyramid.

Since the pyramid is correct, ABCD is a square. Then Savsd = AB ^ 2 = 12 ^ 2 = 144 cm2.

The apothem of a pyramid is the height of its lateral face.

Let’s calculate the area of the side face of HRV. Svsr = BC * RN / 2 = 12 * 8/2 = 48 cm2.

Then the area of the side surface of the pyramid is equal to: Side = 4 * Svav = 4 * 48 = 192 cm2.

The total surface area is: Sпов = Sсн + Side = 144 + 192 = 336 cm2.

Answer: The total surface area is 336 cm2.

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