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

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. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.