In a regular triangular pyramid, the side of the base is 6√5, and the length of the side rib is 16.
| February 3, 2021 | education
In a regular triangular pyramid, the side of the base is 6√5, and the length of the side rib is 16. Find the height of the pyramid.
Since the pyramid is regular, the equilateral triangle ABC lies at its base.
Determine the height of an equilateral triangle through its side.
АН = ВС * √3 / 2 = 6 * √5 * √3 / 2 = 3 * √15 cm.
In an equilateral triangle ABC, the height AH is also its median, which at point O is divided in the ratio 2 / 1. Then AO = 2 * AH / 3 = 2 * 3 * √15 / 3 = 2 * √15 cm.
In a right-angled triangle AOD, according to the Pythagorean theorem, we determine the length of the leg DO.
DO ^ 2 = YES ^ 2 – AO ^ 2 = 256 – 60 = 194.
DO = 14 cm.
Answer: The height of the pyramid is 14 cm.
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