Question

5 Знайдіть площу повної поверхні прямокутного парале- лепіпеда, якщо сторони основ дорівнюють 3 см і 6 см, 3√6 см. діагональ паралелепіпеда​

Answer 1

Ответ:Площа повної поверхні прямокутного паралелепіпеда складає (36 + 108√6) см².

Объяснение:На фото

Answer 2

Finding the Surface Area of a Rectangular Parallelepiped

To find the surface area of a rectangular parallelepiped, we need to calculate the areas of all its six faces and then sum them up.

Let's denote the lengths of the three sides of the base of the parallelepiped as a, b, and c. The lengths of the three sides of the parallelepiped itself are denoted as x, y, and z.

In this case, we are given the following dimensions: - The sides of the base of the parallelepiped: a = 3 cm, b = 6 cm, and c = 3√6 cm. - The diagonal of the parallelepiped: not provided.

To find the surface area, we need to calculate the areas of the six faces of the parallelepiped.

Calculation

1. The area of the top face: a * b. 2. The area of the bottom face: a * b. 3. The area of the front face: b * c. 4. The area of the back face: b * c. 5. The area of the left face: a * c. 6. The area of the right face: a * c.

To find the diagonal of the parallelepiped, we can use the Pythagorean theorem. The diagonal is the hypotenuse of a right triangle formed by the three sides of the parallelepiped. Let's denote the diagonal as d.

Using the Pythagorean theorem, we have:

d^2 = a^2 + b^2 + c^2

Now, let's substitute the given values into the formulas to find the surface area and the diagonal.

Calculation Example

Given: - a = 3 cm - b = 6 cm - c = 3√6 cm

1. The area of the top face: a * b = 3 cm * 6 cm = 18 cm^2. 2. The area of the bottom face: a * b = 3 cm * 6 cm = 18 cm^2. 3. The area of the front face: b * c = 6 cm * 3√6 cm. 4. The area of the back face: b * c = 6 cm * 3√6 cm. 5. The area of the left face: a * c = 3 cm * 3√6 cm. 6. The area of the right face: a * c = 3 cm * 3√6 cm.

To find the diagonal, we can use the Pythagorean theorem:

d^2 = a^2 + b^2 + c^2 = 3^2 + 6^2 + (3√6)^2

Simplifying the equation:

d^2 = 9 + 36 + 54 = 99

Taking the square root of both sides:

d = √99 ≈ 9.9499 cm

Therefore, the surface area of the rectangular parallelepiped is the sum of the areas of all six faces:

Surface Area = 2 * (a * b) + 2 * (b * c) + 2 * (a * c) = 2 * (18 cm^2) + 2 * (6 cm * 3√6 cm) + 2 * (3 cm * 3√6 cm).

Please note that the exact value of the surface area depends on the value of √6, which is an irrational number.