Find the full surface of a regular triangular prism, the side of the base of which is 15 cm, and the side edge is 10 cm.

The area of ​​the lateral surface of a regular prism is equal to the product of the length of the lateral rib and the perimeter of the base. Since an equilateral triangle lies at the base of a regular triangular prism, its perimeter is P = a * 3 = 15 * 3 = 45 cm.

Sside = P * h = 45 * 10 = 450 cm2.

In an equilateral triangle, all angles are 60 °, the base area is determined by the formula:

Sb = 0.5 * a ^ 2 * sin 60 ° = 0.5 * 15 ^ 2 * (√3 / 2) = 225√3 / 4 cm2.

The total surface area of ​​a given prism is equal to the sum of the lateral surface areas and two bases:

Sful = Sside + Sbn = 450 + 2 * 225√3 / 4 = 450 + 225√3 / 2 ≈ 644.86 cm2.