In a straight parallelepiped, the side edge is 2 m, the sides of the base are 11 dm

| August 8, 2021 | education

In a straight parallelepiped, the side edge is 2 m, the sides of the base are 11 dm, and the diagonals of the base are 2: 3. Find the areas of the diagonal sections.

Since at the base of a parallelepiped lies a parallelogram, the sum of the lengths of the squares of its diagonals is equal to the sum of the lengths of the squares of its sides.

Let the diagonal BD = 2 * X dm, then AC = 3 * X dm.

(2 * X) ^ 2 + (3 * X) ^ 2 = 2 * (AB ^ 2 + AD ^ 2).

4 * X ^ 2 + 9 * X ^ 2 = 2 * (121 + 529).

13 * X ^ 2 = 1300.

X ^ 2 = 100.

X = 10.

Then BD = 2 * 10 = 20 dm = 2 m.

AC = 3 * 10 = 30 dm = 3 m.

Diagonal sections are rectangles AA1C1C and BB1D1D.

Sаа1с1с = АС * АА1 = 3 * 2 = 6 m2.

Svv1d1d = BD * BB1 = 2 * 2 = 4 m2.

Answer: The area of the diagonal section is 4 m2 and 6 m2.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.