Question

Площадь диагонального сечения прямоугольного паралилепипеда равна 35 см Найдите площадь боковой поверхности паралилепипеда если стороны основания 3 см и 4 см

Answer 1

1) 35 = 5 * 7, тогда диагональ = 5 см –гипотенуза египетского треугольника, являющегося частью основания
а = 4 см, b = 3 см, с = 7 см
S пов = 2ab + 2bc + 2ac
S пов = 2*4*3 + 2*3*7 + 2*4*7 = 24 + 42 + 56 = 122 см
Ответ: S пов = 122 см

Answer 2

Calculation of the lateral surface area of a rectangular parallelepiped

To find the lateral surface area of a rectangular parallelepiped, we need to know the dimensions of its base and the length of its diagonal cross-section.

Given: - The diagonal cross-section of the parallelepiped has a length of 35 cm. - The sides of the base measure 3 cm and 4 cm.

To calculate the lateral surface area, we can use the formula:

Lateral Surface Area = Perimeter of the Base x Height

The perimeter of the base can be calculated by adding the lengths of all four sides of the base. In this case, the base is a rectangle, so the perimeter is given by:

Perimeter of the Base = 2 x (Length + Width)

Let's calculate the perimeter of the base first:

Perimeter of the Base = 2 x (3 cm + 4 cm) = 2 x 7 cm = 14 cm

Now, we need to find the height of the parallelepiped. Since the diagonal cross-section is given, we can use the Pythagorean theorem to find the height.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the diagonal is the hypotenuse, and the lengths of the other two sides are the lengths of the base (3 cm and 4 cm).

Let's calculate the height using the Pythagorean theorem:

Height = √(Diagonal^2 - Base Length^2)

Height = √(35 cm^2 - (3 cm)^2 - (4 cm)^2) = √(1225 cm^2 - 9 cm^2 - 16 cm^2) = √(1200 cm^2) = 34.64 cm

Now that we have the perimeter of the base (14 cm) and the height (34.64 cm), we can calculate the lateral surface area:

Lateral Surface Area = Perimeter of the Base x Height = 14 cm x 34.64 cm = 484.96 cm^2

Therefore, the lateral surface area of the parallelepiped is approximately 484.96 cm^2.

Please note that the calculations are based on the given dimensions and assumptions.