Lateral ribs of a regular quadrangular pyramid are 4 cm and consists of a base plane at an angle of 60 degrees. Find the volume.

univerkov | February 23, 2021 | education

The angle of the OMВ of the triangle is (90 – 60) = 30, then the OB is equal to half the length of the hypotenuse of the ВM.

ОВ = ВМ / 2 = 4/2 = 2 cm.

Sin600 = OM / BM.

ОМ = ВМ * Sin60 = 4 * √3 / 2 = 2 * √3 cm.

Since there is a square at the base of the pyramid, its diagonals are equal and at the point of intersection they are divided in half, then the ВOС triangle is rectangular and equilateral.

СВ ^ 2 = OB ^ 2 + OС ^ 2 = 4 + 4 = 8.

СВ= √8 = 2 * √2 cm.

The area of the base of the pyramid is equal to: Sbn = СВ ^ 2 = 8 cm2. Then V = Sosn * ОМ / 3 = 8 * 2 * √3 / 3 = 16 * √3 / 3 cm3.

Answer: The volume of the pyramid is 16 * √3 / 3 cm3.

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