# In a regular quadrangular prism, the diagonal of the side face is 23 cm, and the diagonal

In a regular quadrangular prism, the diagonal of the side face is 23 cm, and the diagonal of the base is 20 cm. find the diagonal of the prism.

There is a square at the base of a regular prism, then through the length of the AC diagonal we determine the length of the base of the square.

AC ^ 2 = AD ^ 2 + CD ^ 2 = 2 * AD ^ 2 = 400.

AD ^ 2 = 400/2 = 200.

АD = СD = 10 * √2 cm.

From the right-angled triangle CDD1, we determine the length of the leg DD1.

DD1 ^ 2 = CD1 ^ 2 – CD ^ 2 = 529 – 200 = 329.

Knowing all the dimensions of the parallelepiped, we determine its diagonal.

AC1 ^ 2 = AD ^ 2 + CD ^ 2 + DD1 ^ 2 = 200 + 200 + 329 = 729.

AC1 = 27 cm.

Answer: The length of the diagonal of the parallelepiped is 27 cm.

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