In a regular hexagonal pyramid, the side edge is 20 cm and is inclined

| June 9, 2021 | education

In a regular hexagonal pyramid, the side edge is 20 cm and is inclined to the base plane at an angle of 60 degrees. Find the volume of the pyramid.

The top of the pyramid, point P is projected to point O, the intersection point of the diagonals of the hexagon. The APO triangle is rectangular, in which the angle PAO = 60, the angle APO = 30, then the leg AO, which lies opposite the angle 30, is equal to half the length of the AP hypotenuse.

AO = AP / 2 = 20/2 = 10 cm. Cathetus RO = AH * Sin600 = 20 * √3 / 2 = 10 * √3cm.

At the base of the pyramid lies a regular hexagon, the area of ​​which is:

Sosn = 3 * √3 a^2 / 2, where a is the side of the hexagon.

In a regular hexagon, the length of its side is equal to half the length of its larger diagonal.

AO = AB.

Sb = 3 * √3 * 10^2/2 = 150 * √3 cm2.

Let’s define the volume of the pyramid. V = Sbase * PO / 3 = 150 * √3 * 10 * √3 / 3 = 1500 cm3.

Answer: The volume of the pyramid is 1500 cm3.



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