ABCA1B1C1 is a regular triangular prism, in which AB = 2 √3, AA1 = 4 cm. Find the total surface area of the prism.

Since the prism is correct, at its base lies an equilateral triangle with a side of 2 * √3 cm.

The area of an equilateral triangle is equal to: Savs = Sosn = a ^ 2 * √3 / 4, where a is the length of the side of the triangle.

Sb = (2 * √3) ^ 2 * √3 / 4 = 12 * √3 / 4 = 3 * √3 cm2.

The area of the lateral surface of the prism will be equal to: Sside = Ravs * AA1 = 3 * AB * AA1 = 3 * 2 * √3 * 4 = 24 * √3 cm.

Then Sпов = 2 * Sсн + Side = 2 * 3 * √3 + 24 * √3 = 30 * √3 cm2.

Answer: The total surface area is 30 * √3 cm2.