The height of a regular triangular pyramid is 12cm, the height of the base is 15cm. Find the total surface area of the pyramid.

| February 17, 2021 | education

Since the pyramid is regular, an equilateral triangle lies at its base.

The height of an equilateral triangle is: AH = a * √3 / 2, where a is the side of the triangle, then a = BC = 2 * AH / √3 = 2 * 15 / √3 = 10 * √3 cm.

In a regular triangular pyramid, an equilateral triangle lies at the base, then its medians ВC and AH at point O are divided in the ratio of 2/1, then HO = AH / 3 = 15/3 = 5 cm.

In a right-angled triangle DOН, according to the Pythagorean theorem, DН ^ 2 = OD ^ 2 + HO ^ 2 = 144 + 25 = 169.

DН = 13 cm.

Determine the area of ​​the ВСD triangle. Svsd = ВС * DН / 2 = 10 * √3 * 13/2 = 65 * √3 cm2.

Then Sside = 3 * Svsd = 3 * 65 * √3 = 195 * √3 cm2.

Determine the base area. Sbn = ВС * АН / 2 = 10 * √3 * 15/2 = 75 * √3 cm2.

Spov = S main + S side = 75 * √3 + 195 * √3 = 270 * √3 cm2.

Answer: The surface area of ​​the cone is 270 * √3 cm2.



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