In a regular quadrangular pyramid, the lateral surface area is 120. Apothem is 8. Find the side of the base.

univerkov | March 1, 2021 | education

Since the pyramid is regular, there is a square at its base, and the side faces of the pyramid are equal-sized isosceles triangles.

Then the area of the BCM triangle will be equal to: Svcm = S side / 4 = 120/4 = 30 cm2.

Apothem MН of the pyramid is the height of the BCM triangle, then Svcm = BC * MН / 2 = 30 cm2.

BC = 2 * 30 / MH = 60/8 = 7.5 cm.

Answer: The side of the base of the pyramid is 7.5 cm.

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