# In a rectangular parallelepiped, the sides of the base are 10 cm and 17 cm; one of the base diagonals is 21 cm;

In a rectangular parallelepiped, the sides of the base are 10 cm and 17 cm; one of the base diagonals is 21 cm; the largest diagonal of the parallelepiped is 29 cm. Determine the full surface of the parallelepiped.

Let us determine the area of the AСD triangle at the base of the AВСD by Heron’s theorem.
The half-perimeter of the triangle is: p = (17 + 21 + 10) / 2 = 48/2 = 24 cm.
Then Sacd = 24 * (24 – 21) * (24 – 17) * (24 – 10) = 24 * 3 * 7 * 14 = 7056 = 84 cm2.
Then Sbn = 2 * Sacd = 2 * 84 = 168 cm2.
From the right-angled triangle ACC1, according to the Pythagorean theorem, we determine the leg CC1.
CC12 = AC12 – AC2 = 841 – 441 = 400.
CC1 = 20 cm.
Let’s define the lateral surface area. Side = Ravsd * CC1 = 54 * 20 = 1080 cm2.
Then Sпов = 2 * Sсн + S side = 336 + 1080 = 1416 cm2.
Answer: The surface area is 1416 cm2.

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.