In a regular quadrangular prism, the base area is 225 cm2 and the height is 10 cm, find the diagonal of the prism.
September 7, 2021 | education
| Since the prism is correct, there are squares at its bases.
Let us define, through the area, the length of the side of the base of the prism.
Sosn = AB ^ 2 = 225.
AB = 15 cm.
We construct the diagonal AC of the square, and by the Pythagorean theorem we determine its length.
AC ^ 2 = AB ^ 2 + AD ^ 2 = 225 + 225 = 450.
AC = √288 = 15 * √2 cm.
Triangle ACC1 is rectangular, then AC1 ^ 2 = AC ^ 2 + CC1 ^ 2 = 450 + 100 = 550.
AC1 = √550 = 5 * √22 cm.
Answer: The diagonals of the prism are 22 5 * √22 cm.
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