In the rectangular parallelepiped ABCDA1B1C1D1 the lengths of the edges are known: AB = 12; AD = 8; AA1 = 15.

In the rectangular parallelepiped ABCDA1B1C1D1 the lengths of the edges are known: AB = 12; AD = 8; AA1 = 15. Find the area of the section passing through the vertices A, b, C1.

Since the parallelepiped is straight, its side faces are rectangles.

Then the triangle ВСС1 is rectangular, in which, according to the Pythagorean theorem, we determine the length of the hypotenuse ВС1.

BC1 ^ 2 = BC ^ 2 + CC1 ^ 2 = 8 ^ 2 + 15 ^ 2 = 64 + 225 = 289.

BC1 = 17 cm.

The desired section is a rectangle ABC1D1, then its area will be equal to:

Ssection = AB * BC1 = 12 * 17 = 204 cm2.

Answer: The cross-sectional area is 204 cm2.