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

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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