In a regular quadrangular prism, the base area is 169 cm2 and the height is 15 cm, find the diagonal of the prism.

univerkov | September 18, 2021 | education

Since the prism is correct, there is a square at its base. By condition, the area of the base of the prism is 169 cm2, then the side of the square will be: AB = BC = CD = AD = √169 = 13 cm.

We draw a diagonal AC of the base, then AC ^ 2 = AD ^ 2 + CD ^ 2 = 338.

AC = 2 * √13.

From the right-angled triangle ACA1, we find the length of the hypotenuse CA1.

CA1 ^ 2 = AA1 ^ 2 + AC ^ 2 = 225 + 338 = 563.

CA1 = √563 cm.

Answer: The diagonal of the prism is √563 cm.

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