In the rectangular parallelepiped ABCDA1B1C1D1, the lengths of the edges are known: AB = 27, AD = 36, AA1 = 10.

In the rectangular parallelepiped ABCDA1B1C1D1, the lengths of the edges are known: AB = 27, AD = 36, AA1 = 10. Find the area of the section passing through the vertices D, D1 and B.

Section DBB1D1 is a rectangle, BB1 = DD1, BD = B1D1. The DD1 edge is equal to the AA1 edge, which is equal to 10.
Calculate the side of the rectangle BD, which is the hypotenuse in the right-angled triangle ABD. We know the values of the legs of the triangle AB = 27, AD = 36. Let’s calculate the hypotenuse according to the Pythagorean theorem:
BD ^ 2 = AB ^ 2 + AD ^ 2 = 27 ^ 2 + 36 ^ 2 = 729 + 1296 = 2025;
BD = 45;
Find the area of the rectangle DBB1D1:
45 * 10 = 450.
Answer: the cross-sectional area is 450.