# The sum of the lengths of all the edges of the rectangular parallelepiped is equal to 84 cm

The sum of the lengths of all the edges of the rectangular parallelepiped is equal to 84 cm of its lengths 9 cm width 7 cm find the volume of the parallelepiped.

Given:
P (ABCDA1B1C1D1) = 84 cm
AD = BC = A1D1 = B1C1 = 9 cm
AB = DC = A1B1 = D1C1 = 7 cm

Find:
V (ABCDA1B1C1D1) -?

1) The perimeter of a rectangular parallelepiped is calculated using the following formula:
P (ABCDA1B1C1D1) = 4 * AD + 4 * AB + 4 * AA1;
2) Calculate the height of the rectangular parallelepiped:
AA1 = (P (ABCDA1B1C1D1) – 4 * AD – 4 * AB) / 4 = (84 – 4 * 9 – 4 * 7) / 4 = 5 (cm);
3) Calculate the volume of a rectangular parallelepiped:
V (ABCDA1B1C1D1) = AD * AB * AA1 = 9 * 7 * 5 = 315 (cm3).

Answer: The volume of a rectangular parallelepiped is 315 cm3. 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.