The pyramid is crossed by a plane parallel to the base. The base area is 1690 dm2, and the cross-sectional

| May 20, 2021 | education

The pyramid is crossed by a plane parallel to the base. The base area is 1690 dm2, and the cross-sectional area is 10 dm2. In what relation, counting from the top, the section plane divides the height of the pyramid?

A pyramid is a polyhedron, the base of which is an arbitrary polygon, and the side faces are triangles with a common vertex.
Let the height of a pyramid with a base area of ​​1690 m² be equal to 1, then to find the height of a pyramid with a base area of ​​10 m², we will make the proportion:
1690 – 1
10 – x
Based on the basic rule of proportion, according to which the product of the extreme terms of the proportion is equal to the product of the means, we compose an equation.
1690 * x = 10 * 1
x = 10 * 1/1690
x = 1/169
Thus, a plane parallel to the base intersects the height of the pyramid at 1/169 of the height of the pyramid, counting from the top. Then, to find the remaining lower part of the height of the pyramid, it is necessary to subtract the height of the upper part from the entire height of the pyramid:
1-1 / 169 = (169-1) / 169 = 168/169
In order to find the ratio into which the height of the pyramid is divided by the plane, we divide the upper part of the height by the lower one. Then
(1/169) / (168/169) = 1/169 * 169/168 = 1/168
Answer: 1/168



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