# In a regular parallelepiped, the base area is 144 cm2, and the height is 14 cm

In a regular parallelepiped, the base area is 144 cm2, and the height is 14 cm, determine the diagonal of the parallelepiped and the area of the flat surface of the parallelepiped.

Since the parallelepiped is regular, there is a square at its base. Let us determine the length of the side of the base of the parallelepiped if the area of ​​the base is 144 cm2. AB = BC = DC = AD = √144 = 12 cm.

Consider a right-angled triangle ABD, whose legs are 12 cm.Let’s find the hypotenuse BD.

BD ^ 2 = AD ^ 2 + AB ^ 2 = 144 + 144 = 288.

ВD = 12 * √2.

Consider a right-angled triangle BDD1, whose leg DD1 is equal to the height of the parallelepiped DD1 = 14 cm, leg BD = 12 * √2, and the hypotenuse D1B is the parallelepiped’s diagonal.

D1B ^ 2 = DD1 ^ 2 + DB ^ 2 = 142 + (12 * √2) 2 = 196 + 288 = 484.

D1B = 22 cm.

Determine the surface area of ​​the parallelepiped.

S = 2 * AB ^ 2 + 4 * AB * AA1 = 2 * 144 + 4 * 12 * 14 = 288 + 672 = 960 cm2.

Answer: D1B = 22 cm. S = 960 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.