At the base of the rectangular parallelepiped lies a square with a side of 2 cm.

| September 8, 2021 | education

At the base of the rectangular parallelepiped lies a square with a side of 2 cm. The diagonal of the parallelepiped is 3 cm. Find the total surface area of the parallelepiped.

At the base of the prism, we draw a diagonal ВD and, according to the Pythagorean theorem, knowing the lengths of the sides of the square, we determine its length. ВD ^ 2 = АD ^ 2 + AB ^ 2 = 4 + 4 = 8. ВD = 2 * √2 cm.

From the right-angled triangle BB1D, we determine the height of the prism BB1 by the Pythagorean theorem.

BB1 ^ 2 = DV1 ^ 2 – BD ^ 2 = 9 – 8 = 1. BB1 = 1 cm.

Determine the area of the base of the prima Sb = AB * AD = 2 * 2 = 4 cm2.

Let us determine the area of the lateral surface of the prism. Sside = Ravsd * BB1 = 4 * AB * BB1 = 4 * 2 * 1 = 8 cm2.

Determine the total area of the prism. S floor = 2 * Sb + S side = 2 * 4 + 8 = 16 cm2.

Answer: The total surface area is 16 cm2.



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