In a regular triangular pyramid, the height is 2√3, the side face is inclined to the base

| May 5, 2021 | education

In a regular triangular pyramid, the height is 2√3, the side face is inclined to the base plane at an angle of 60 degrees. Is the volume of the pyramid?

In a right-angled triangle DOH, we determine the length of the OH leg.

tgun = DO / НO.

HO = DO / tg60 = 2 * √3 / √3 = 2 cm.

Since triangle ABC is equilateral, its heights, at point O, are divided in the ratio 2 / 1. Then, AO = 2 * OH = 2 * 2 = 4 cm, AH = AO + OH = 4 + 2 = 6 cm.

Let us define its sides through the shape of the height of an equilateral triangle.

AH = BC * √3 / 2.

BC = 2 * AN / √3 = 2 * 6 / √3 = 4 * √3 cm.

The area of an equilateral triangle is equal to: Sav = BC2 * √3 / 4 = 48 * √3 / 4 = 12 * √3 cm2.

Then V = Saws * DO / 3 = 12 * √3 * 2 * √3 / 3 = 24 cm3.

Answer: The volume of the pyramid is 24 cm3.



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