The height of a regular quadrangular pyramid is 12 cm, and the size of the dihedral rib at the base

univerkov | September 12, 2021 | education

The height of a regular quadrangular pyramid is 12 cm, and the size of the dihedral rib at the base of the pyramid is 30⁰. Find the total surface area of the pyramid.

Consider a right-angled triangle SOK, in which SO = 12 cm, the angle SKO is 30. Then the hypotenuse of SO is equal to two sizes of the leg located opposite the angle 30.

SK = 2 * SO = 2 * 12 = 24 cm. Find the size of the leg OK, which is half the side of the base of the pyramid.

OK = SO * Ctg 30 = 12 * √3.

Then the side of the base AD = AB = BC = CD = 2 * 12 √3 = 24 * √3.

S floor = S main + S side = (24 * √3) 2 + ((4 * 24 * √3) * 24) / 2 = 1728 + 1152 * √3.

Answer: S = 1728 + 1152 * √3.

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