In the rectangular parallelepiped ABCDA1B1C1D1, the lengths of the edges AB = 15, AD = 8, AA1 = 21 are known.

In the rectangular parallelepiped ABCDA1B1C1D1, the lengths of the edges AB = 15, AD = 8, AA1 = 21 are known. Find the area of the section through vertices B, B1, D.

The section will be rectangle BB1D1D, where BB1 = 21. Side BD is the diagonal of rectangle ABCD. Its length can be found by the Pythagorean theorem:

BD = √ (AB² + AD²).

Find BD:

BD = √ (15² + 8²) = √ (225 + 64) = √289 = 17.

The area of the rectangle BB1D1D is:

Sbb1d1d = BD * BB1.

We know both sides, let’s find the area:

Sbb1d1d = 17 * 21 = 357.

Answer: The cross-sectional area through vertices B, B1 and D is 357.