A regular triangle lies at the base of a triangular pyramid. Its side is 12 cm

univerkov | July 29, 2021 | education

A regular triangle lies at the base of a triangular pyramid. Its side is 12 cm. The height of the pyramid is 10 kora out of two. What is the volume of the pyramid?

Since a regular triangle lies at the base of the pyramid, then AB = BC = AC = 12 cm.

The area of a regular triangle is determined by the formula:

Sop = a ^ 2 * √3 / 4, where a is the side length of a regular triangle.

Sbn = AB ^ 2 * √3 / 4 = 12 ^ 2 * √3 / 4 = 36 * √3 cm2.

Then the volume of the pyramid will be equal to:

V = Sbas * SO / 3 = 36 * √3 * 10 * √2 / 3 = 120 * √6 cm3.

Answer: The volume of the pyramid is 120 * √6 cm3.

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