# The base side of a regular triangular prism is a, the side edge is b, find the total surface area of the prism.

In a regular prism, at the base lies an equilateral triangle AB = BC = AC = a cm, and its lateral faces are rectangles with sides a and b.

Let us determine the area of ​​the lateral surface of the prism.

Sside = P * h, where P is the perimeter of the triangle at the base, h is the height of the prism, it is also the height of the side face. Sside = 3 * a * b cm2.

The area of ​​the base of the prism is calculated by the formula for the area of ​​an equilateral triangle: Sbn = a ^ 2 * √3 / 4 cm2.

Determine the total surface area of ​​the prism.

S floor = S side + 2 * S main = 3 * a * b + 2 * a ^ 2 * √3 / 4 = 3 * a * b + a ^ 2 * √3 / 2 cm2.

Answer: The total surface area is 3 * a * b + a ^ 2 * √3 / 2 cm2.

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