In a regular triangular pyramid, the flat angle at the apex is 60 degrees, and the height of the pyramid

| August 5, 2021 | education

In a regular triangular pyramid, the flat angle at the apex is 60 degrees, and the height of the pyramid is 4 cm. Find the area of the side surface of the pyramid.

The lateral faces of a regular pyramid are equilateral triangles, and since the flat angle at the apex of the pyramid is 60, the lateral faces of the pyramid are equilateral triangles, and therefore the pyramids are a tetrahedron.

From the formula for the height of a tetrahedron, we determine the length of its faces.

DO = BC * √6 / 3.

BC = 3 * DO / √6 = 12 / √6 = 2 * √6 cm.

Since the side faces of the pyramid are equilateral triangles, then Sdvs = BC ^ 2 * √3 / 4 = 24 * √3 / 4 = 6 * √3 cm2.

Then Sside = 3 * Sdvs = 3 * 6 * √3 = 18 * √3 cm2.

Answer: The lateral surface area is 18 * √3 cm2.



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