In a regular triangular pyramid, the side of the base is 6 cm and the height is 10 cm.

| May 16, 2021 | education

In a regular triangular pyramid, the side of the base is 6 cm and the height is 10 cm. Determine the full surface of the pyramid.

The total surface area is equal to the sum of the base area and the lateral surface area.

S = S main + S side.

Since an equilateral triangle lies at the base, then Sbasn = AC ^ 2 * √3 / 4 = 6 ^ 2 * √3 / 4 = 9 * √3.

Apothem SD area of ​​the side face of the pyramid. In triangle SOD, leg OD is the radius of a circle inscribed in triangle ABC. OD = SВ / 2 * √3 = 6/2 * √3 = = 3 / √3 = √3.

Let us find apothem SD by the Pythagorean theorem.

SD ^ 2 = SO ^ 2 + OD ^ 2 = 100 + 3 = 103.SD = √103.

Let us find the area of ​​the lateral surface, which is equal to half the product of the base perimeter and the apothem.

Sside = Ravs * SD / 2 = 3 * 6 * √103 / 2 = 9 * √103.

S = 9 * √3 + 9 * √103 = 9 * (√3 + √103).

Answer: S = 9 * (√3 + √103).



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