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.