Question

Радиус окружности описанной около основания правильной треугольной призмы равен 2 корня из 3 см. НАйти Sбок, если все боковые грани квадраты

Answer 1

Прикрепляю листочек.....................................

Answer 2

Problem Analysis

We are given that the radius of the circle circumscribed around the base of a regular triangular prism is equal to 2√3 cm. We need to find the surface area of the lateral faces of the prism, given that all the lateral faces are squares.

Solution

To find the surface area of the lateral faces of the prism, we first need to find the length of the sides of the square faces. Let's denote the side length of the square as s.

Since the base of the prism is a regular triangle, we can use the relationship between the radius of the circumscribed circle and the side length of the triangle. For a regular triangle, the radius of the circumscribed circle is equal to the product of the side length and √3 divided by 3.

Let's use this relationship to find the side length of the triangle:

2√3 = s * √3 / 3

To solve for s, we can multiply both sides of the equation by 3 and divide by √3:

2√3 * 3 / √3 = s

Simplifying the equation:

6 = s

So, the side length of the square faces of the prism is 6 cm.

To find the surface area of the lateral faces, we need to find the area of one square face and multiply it by the number of square faces. Since all the lateral faces are squares, the area of one square face is equal to the square of the side length.

The surface area of the lateral faces is given by:

S_lateral = 4 * (s^2)

Substituting the value of s:

S_lateral = 4 * (6^2)

Calculating the value:

S_lateral = 4 * 36 = 144 cm^2

Therefore, the surface area of the lateral faces of the prism is 144 cm^2.

Answer

The surface area of the lateral faces of the prism is 144 cm^2.