# Equilateral triangle with side A, rotates around one of the sides. What shape of rotation is obtained

July 26, 2021 | education

| **Equilateral triangle with side A, rotates around one of the sides. What shape of rotation is obtained in this case? Find its surface area.**

Since the triangle is equilateral, then when rotating around any of its sides, the area of the resulting figure will not change.

The figure of rotation will be two symmetrical cones with one base.

The length of the generatrix of the cones is equal to the length of the side of the triangle, and the radius of the circle is equal to half this length.

Let us determine the area of the lateral surface of one cone.

S side = AB * n * OA = n * a ^ 2/2.

Then the surface area of the whole figure will be equal to: S = 2 * n * a ^ 2/2 = n * a ^ 2.

Answer: The area of the rotation figure is equal to n * a ^ 2.

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