Question

Дан прямоугольный параллелепипед, стороны основания которого 72 и 21 дм, а высота - 24 дм. Найти площадь диагонального сечения.

Answer 1

В основании лежит прямоугольник, по теореме Поясните находим гипотезу, она равна 75.Диагональное течение это прямоугольник 24*75=1800

Answer 2

Problem Analysis

We are given a rectangular parallelepiped with base sides measuring 72 dm and 21 dm, and a height of 24 dm. We need to find the area of the diagonal section.

Solution

To find the area of the diagonal section, we first need to find the length of the diagonal of the rectangular parallelepiped. We can use the Pythagorean theorem to calculate the length of the diagonal.

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the diagonal of the rectangular parallelepiped is the hypotenuse of a right-angled triangle, and the sides of the triangle are the length, width, and height of the parallelepiped.

Let's calculate the length of the diagonal using the Pythagorean theorem:

Step 1: Calculate the square of the length of the diagonal: - Length of the diagonal squared = (Length of the base)^2 + (Width of the base)^2 + (Height)^2

Step 2: Take the square root of the result from step 1 to find the length of the diagonal.

Step 3: Once we have the length of the diagonal, we can calculate the area of the diagonal section by multiplying the length of the diagonal by the height of the parallelepiped.

Let's calculate the length of the diagonal and the area of the diagonal section:

Step 1: Calculate the square of the length of the diagonal: - Length of the diagonal squared = (72 dm)^2 + (21 dm)^2 + (24 dm)^2

Step 2: Take the square root of the result from step 1 to find the length of the diagonal.

Step 3: Calculate the area of the diagonal section: - Area of the diagonal section = Length of the diagonal * Height

Calculation

Let's perform the calculations:

Step 1: Calculate the square of the length of the diagonal: - Length of the diagonal squared = (72 dm)^2 + (21 dm)^2 + (24 dm)^2 - Length of the diagonal squared = 5184 dm^2 + 441 dm^2 + 576 dm^2 - Length of the diagonal squared = 6201 dm^2

Step 2: Take the square root of the result from step 1 to find the length of the diagonal: - Length of the diagonal = √(6201 dm^2) - Length of the diagonal ≈ 78.74 dm

Step 3: Calculate the area of the diagonal section: - Area of the diagonal section = Length of the diagonal * Height - Area of the diagonal section ≈ 78.74 dm * 24 dm - Area of the diagonal section ≈ 1889.76 dm^2

Answer

The area of the diagonal section of the rectangular parallelepiped is approximately 1889.76 square decimeters.

Please let me know if I can help you with anything else.