An equilateral triangle with a side of 14 cm lies at the base of a regular pyramid.
| April 2, 2021 | education
An equilateral triangle with a side of 14 cm lies at the base of a regular pyramid. Find the apothem of the side face if the length of the side edge is 8 cm.
Since a regular triangle lies at the base of the pyramid, then AB = BC = AC = 14 cm.
In triangle ABC, we will omit the height BH, which in a regular triangle will also be the median, and therefore AH = CH = AC / 2 = 14/2 = 7 cm.
Consider a right-angled triangle AMН, in which the MН leg will be the desired apothema.
By the Pythagorean theorem, MH ^ 2 = AM ^ 2 – AH ^ 2 = 8 ^ 2 – 7 ^ 2 = 64 – 49 = 15.
MH = √15 cm.
Answer: Apothem of the side face is √15 cm.
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