# Find the volume of a rectangular parallelepiped ABCDA1B1C1D1 if AC1 = 13 cm, BD = 12 cm, BC1 = 11 cm.

From the right-angled triangle ABC1 we determine the length of the leg AB.

AB ^ 2 = AC1 ^ 2 – BC1 ^ 2 = 13 ^ 2 – 11 ^ 2 = 169 – 121 = 48.

AB = √48 = 4 * √3 cm.

From the right-angled triangle ABD we determine the length of the leg AD.

AD ^ 2 = BD ^ 2 – AB ^ 2 = 144 – 48 = 96.

AD = √96 = 4 * √6 cm.

In a right-angled triangle BCC1, we determine the length of the CC1 leg.

CC1 ^ 2 = BC1 ^ 2 – CB ^ 2 = 121 – 96 = 25.

CC1 = 5 cm.

Let’s define the volume of the parallelepiped.

V = AВ * AD * CC1 = 4 * √3 * 4 * √6 * 5 = 80 * √18 = 240 * √2 cm3.

Answer: The volume of a parallelepiped is 240 * √2 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.