The base side of a regular triangular prism is 2 roots of 3 and the height is 5 cm, find the volume of the prism.

The volume of a regular triangular prism can be found as follows:

V = Sb * h, where Sb is the area of ​​the base, and h is the height of the prism.

An equilateral triangle lies at the base of a regular triangular prism. Its area can be found using the following formula:

Sosn = a²√3 / 4, where a is the side of the triangle.

Find the area of ​​the triangle lying at the base of the prism:

Sb = ((2√3) ² * √3) / 4 = (4 * 3 * √3) / 4 = 3√3 ≈ 5.2 cm².

Now that we know the base area and height of the prism, we can find its volume. Let’s calculate it:

V ≈ 5.2 * 5 ≈ 26 cm³.

Answer: The volume of a regular triangular prism is approximately 26 cubic centimeters.