In a regular triangular prism, the side of the base is 6 cm, the lateral edge is 12 cm.

univerkov | August 31, 2021 | education

In a regular triangular prism, the side of the base is 6 cm, the lateral edge is 12 cm. Find the total surface area of the prism?

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

The area of an equilateral triangle is: Sbasn = AB ^ 2 * √3 / 4 = 36 * √3 / 4 = 9 * √3 cm2.

Determine the perimeter of the triangle at the base of the prism. Rosn = 3 * AB = 3 * 6 = 18 cm.

Then S side = Rosn * CC1 = 18 * 12 = 218 cm2.

Let us determine the total surface area of the prism.

Sпов = S side + 2 * Sсн = 216 + 2 * 9 * √3 = 192 + 18 * √3 = 18 * (12 + √3) cm2.

Answer: The total surface area of the prism is 18 * (12 + √3) cm2.

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