What is the total surface area of a regular quadrangular pyramid with a side at the base of 4 cm and an apothem of 5 cm.

univerkov | April 27, 2021 | education

Since, by condition, the pyramid is regular, there is a square at its base, and the side faces of the pyramid are equal to each other and represent isosceles triangles.

Apothem KM of the triangle CDK is the height of this triangle.

The total surface area of the pyramid will be equal to:

Spol = S main + 4 * S side = AD * AB + 4 * (DC * KM) / 2 = 4 * 4 + 4 * (4 * 5) / 2 = 16 * 40 = 56 cm2.

Answer: The area of the pyramid is 56 cm2.

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