Question

Длина всех ребер правильной треугольной призмы равны. Вычислите объем призмы, если периметр её боковой грани равен 48 см. Можно рисунок

Answer 1

Смотри во вложении.

Answer 2

Calculation of the Volume of a Regular Triangular Prism

To calculate the volume of a regular triangular prism, we need to know the length of its edges and the perimeter of its lateral face. In this case, we are given that the length of all the edges of the prism is equal and that the perimeter of the lateral face is 48 cm.

Let's denote the length of each edge of the prism as a.

To find the volume of the prism, we can use the formula:

Volume = (1/4) * √3 * a^2 * h

where h is the height of the prism.

To find the height of the prism, we can use the formula:

Height = (2/√3) * (Perimeter of the lateral face) / 3

Substituting the given value of the perimeter of the lateral face (48 cm) into the formula, we can find the height.

Let's calculate the height first:

Height = (2/√3) * 48 / 3

Using a calculator, we can simplify this expression:

Height = 16√3 cm.

Now that we have the height, we can calculate the volume of the prism:

Volume = (1/4) * √3 * a^2 * h

Substituting the value of the height (16√3 cm) into the formula, we get:

Volume = (1/4) * √3 * a^2 * 16√3

Simplifying this expression, we have:

Volume = 4√3 * a^2 * 16

Volume = 64√3 * a^2

Therefore, the volume of the prism is 64√3 * a^2 cubic centimeters.

Please note that we cannot calculate the exact volume without knowing the length of the edges of the prism. If you have the length of the edges, you can substitute that value into the formula to find the volume.

I hope this helps! Let me know if you have any further questions.