In a rectangular parallelepiped, the sides of the base are 3 cm and 4 cm, and the height of the parallelepiped is 5 cm. Find the area of the diagonal section.
Since the parallelepiped is rectangular, there is a rectangle at its base.
Let us draw the diagonal AC of the parallelepiped’s base and determine its length by the Pythagorean theorem.
AC ^ 2 = AD ^ 2 + CD ^ 2 = 4 ^ 2 + 3 ^ 2 = 16 + 9 = 25.
AC = 5 cm.
The diagonal section of the parallelepiped is a rectangle АА1С1С, then its area will be equal to:
Ssection = AA1 * AC = 5 * 5 = 25 cm2.
Answer: The area of the diagonal section is 25 cm2.
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