The sides of the base of the rectangular parallelepiped are 6 cm and 8 cm.

univerkov | May 23, 2021 | education

The sides of the base of the rectangular parallelepiped are 6 cm and 8 cm. The area of the diagonal section is 70 cm ^ 2. Find the complete surface of this parallelepiped.

Since the parallelepiped is rectangular, all of its faces are rectangles.

Let’s construct a diagonal AC at the base of the parallelepiped.

By the Pythagorean theorem in the right-angled triangle ABC, we determine the length of the hypotenuse AC.

AC ^ 2 = AB ^ 2 + BC ^ 2 = 36 + 64 = 100.

AC = 10 cm.

The diagonal section of a parallelepiped is a rectangle АА1С1С.

Then Ssech = АА1 * АС.

AA1 = Ssection / AC = 70/10 = 7 cm.

Determine the area of the base of the parallelepiped.

Sbn = AB * AD = 6 * 8 = 48 cm2.

Determine the area of the lateral surface of the parallelepiped.

Sside = Ravsd * AA1 = 28 * 7 = 196 cm2.

Then Sпов = 2 * Sсн + Sides = 2 * 48 + 196 = 292 cm2.

Answer: The surface area of the parallelepiped is 292 cm2.

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