The total surface area of a regular quadrangular prism is 210 and the side surface is 160.

univerkov | June 17, 2021 | education

The total surface area of a regular quadrangular prism is 210 and the side surface is 160. What is the length of the diagonal of the base of the prism?

Determine the area of the base of the prism.

Sb = (Sпов – Sbok) / 2 = (210 – 160) / 2 = 50/2 = 25 cm2.

Since the prism is correct, there is a square at its base, then AB = BC = CD = AD = √Sbasn = √25 = 5 cm.

The ACD triangle is rectangular and isosceles, then AC ^ 2 = 2 * AD ^ 2 = 2 * 25.

AC = 5 * √2 cm.

Answer: The length of the diagonal of the base is 5 * √2 cm.

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