In oblique parallelepiped ABCDA1B1C1D1, the side edge is 16. The distance between edge AA1

| May 2, 2021 | education

In oblique parallelepiped ABCDA1B1C1D1, the side edge is 16. The distance between edge AA1 and edges BB1, DD1, and CC1 is 8, 15, and 17. Calculate the volume.

Since the segments A1K, A1M, A1H are perpendicular to the lateral edge, the section A1KMN is perpendicular to the lateral edge AA1.

Then V = Sа1кмн * АА1.

Quadrilateral A1KMN is a parallelogram, the diagonal A1M of which divides it into two equal triangles.

Let us determine the area of the triangle A1KM by Heron’s theorem.

The semi-perimeter of the A1KM triangle is: P = (A1K + KM + MN) / 2 = (8 + 15 + 17) / 2 = 20 cm.

Then Sa1km = 20 * (20 – 8) * (20 – 15) * (20 – 17) = 3600 = 60 cm2.

Then Sa1cmn = 2 * 60 = 120 cm2.

V = Sa1cmn * AA1 = 120 * 16 = 7200 cm3.

Answer: The volume of the parallelepiped is 7200 cm3.



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