# 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.