In the rectangular parallelepiped abcda1b1c1d1, the lengths of the edges AB = 8 AD = 6, AA1 = 14 are known
| May 22, 2021 | education
In the rectangular parallelepiped abcda1b1c1d1, the lengths of the edges AB = 8 AD = 6, AA1 = 14 are known. Find the cross-sectional area of a parallelepiped by a plane passing through points B, B1 and D
The desired section is the diagonal section BB1D1D, which is a rectangle.
From the right-angled triangle ABD, according to the Pythagorean theorem, we determine the length of the hypotenuse BD.
BD ^ 2 = AD ^ 2 + AB ^ 2 = 6 ^ 2 + 8 ^ 2 = 36 + 64 = 100.
ВD = 10 cm.
Let’s define the cross-sectional area.
Svv1d1d = ВD * BB1 = 10 * 14 = 140 cm2.
Answer: The cross-sectional area is 140 cm2.
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