Question

Срочно помогите даю 50 балло и как составит Найти объём правильной треугольной призмы, у которой сторона основания равна 6 см, а диагонально боковой грани равна 62 см.

Answer 1

Ответ:

Пошаговое объяснение:

Площадь основания $\frac{a^{2}\sqrt{3}}{4}$ = 9$\sqrt{3}$

Высота H = √$62^{2}$ - $6^{2}$ = √3808

V = 9√3*√3808 = 36$\sqrt{714}$ =

Answer 2

Finding the Volume of a Right Triangular Prism

To find the volume of a right triangular prism, we need to know the length of the base, the height of the prism, and the length of one of the triangular faces. In this case, we are given the length of the base and the length of the diagonal of one of the triangular faces.

Let's break down the problem and solve it step by step.

Given: - Length of the base of the prism = 6 cm - Length of the diagonal of one of the triangular faces = 62 cm

Step 1: Finding the height of the prism To find the height of the prism, we can use the Pythagorean theorem. The height is the missing side of the right triangle formed by the base and the diagonal of the triangular face.

Let's denote the height as 'h'. According to the Pythagorean theorem, we have:

base^2 + height^2 = diagonal^2

Substituting the given values, we get:

6^2 + h^2 = 62^2

Simplifying the equation:

36 + h^2 = 3844

h^2 = 3808

Taking the square root of both sides:

h ≈ 61.74 cm

So, the height of the prism is approximately 61.74 cm.

Step 2: Finding the volume of the prism The volume of a right triangular prism can be calculated using the formula:

Volume = (1/2) * base * height * length

Substituting the given values, we get:

Volume = (1/2) * 6 cm * 61.74 cm * 62 cm

Simplifying the equation:

Volume ≈ 11418 cm^3

Therefore, the volume of the right triangular prism is approximately 11418 cubic centimeters.

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