Question

СРОЧНО!!! Сторона основи прямого паралелепіпеда дорівнює 2v2 см і 4 см, а один із кутів основи дорівнює 45°.Більша діагональ паралелепіпеда дорівнює 7 см .Знайдіть площу бічної поверхні паралелепіпеда. (Сторона основания прямого параллелепипеда равна 2v2 см и 4 см, а один из углов основания равен 45°. Большая диагональ параллелепипеда равна 7 см. Найдите площадь боковой поверхности параллелепипеда)​

Answer 1

Відповідь:

$24+12\sqrt{2}$см^2

Пояснення:

Відповідь на фото!

Answer 2

To find the lateral surface area of a parallelepiped, we need to know the dimensions of its base and the length of its diagonal. Let's solve the problem step by step.

Given information: - Side of the base of the parallelepiped = 2√2 cm and 4 cm - One of the angles of the base = 45° - Length of the larger diagonal = 7 cm

Finding the Height of the Parallelepiped:

To find the height of the parallelepiped, we can use the Pythagorean theorem. The height is the perpendicular distance between the base and the opposite face of the parallelepiped.

Let's consider the right triangle formed by the base, the height, and the larger diagonal. The base of the triangle is the side of the base of the parallelepiped, and the hypotenuse is the larger diagonal.

Using the Pythagorean theorem, we can find the height as follows:

h^2 = (larger diagonal)^2 - (side of the base)^2 h^2 = 7^2 - (2√2)^2 - 4^2 h^2 = 49 - 8 - 16 h^2 = 25 h = 5 cm

Therefore, the height of the parallelepiped is 5 cm.

Finding the Lateral Surface Area:

The lateral surface area of a parallelepiped can be calculated by multiplying the perimeter of the base by the height.

To find the perimeter of the base, we need to consider the given dimensions of the base. Since one of the angles of the base is 45°, we can determine the lengths of the sides using trigonometric ratios.

Let's consider the right triangle formed by one side of the base, the height, and the diagonal. The base of the triangle is the side of the base of the parallelepiped, and the hypotenuse is the diagonal.

Using trigonometric ratios, we can find the lengths of the sides of the base as follows:

sin(45°) = (side of the base) / (diagonal) sin(45°) = (2√2) / (7) 2√2 = 7 * sin(45°) 2√2 = 7 * (√2 / 2) 2√2 = 7√2 / 2 4√2 = 7√2 4 = 7

This is not possible, as 4 is not equal to 7. Therefore, there seems to be an error in the given information or calculations.

Please double-check the given information and calculations to ensure accuracy.