The sides of the base of the rectangular parallelepiped are equal to 3 and 4. The diagonal of the parallelepiped makes

univerkov | June 15, 2021 | education

The sides of the base of the rectangular parallelepiped are equal to 3 and 4. The diagonal of the parallelepiped makes an angle with the plane of the base, the tangent of which is 1/35. Find the total surface area of the parallelepiped.

Let us construct a diagonal AC at the base of the parallelepiped and, by the Pythagorean theorem, determine its length.

AC ^ 2 = AB ^ 2 + AD ^ 2 = 9 + 16 = 25.

AC = 5 cm.

In a right-angled triangle ACC1 tgCAC1 = CC1 / AC.

CC1 = AC * tgACC1 = 5 * 1/35 = 1/7 cm.

Determine the area of the base of the parallelepiped.

Sbn = AB * AD = 3 * 4 = 12 cm2.

The lateral surface area is: S side = Ravsd * CC1 = 14 * 1/7 = 2 cm2.

Then Sпов = 2 * Sсн + Sbok = 2 * 12 + 2 = 26 cm2.

Answer: The total surface area is 26 cm2.

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