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

In an equilateral triangle ABC, we construct the height of CH, which is also the median of the triangle, then AH = BH = AB / 2 = 2 * √3 / 2 = √3 cm.

In a right-angled triangle ACH, according to the Pythagorean theorem, CH ^ 2 = AC ^ 2 – AH ^ 2 = 12 – 3 = 9.

CH = 3 cm.

Then Savs = AB * CH / 2 = 2 * √3 * 3/2 = 3 * √3 cm2.

Sside = Ravs * AA1 = 3 * 2 * √3 * 4 = 24 * √3 cm2.

Sпов = 2 * Sсн + S side = 2 * 3 * √3 + 24 * √3 = 72 * √3 + 324 = 30 * √3 cm2.

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