求平截头锥体/截棱锥体横截面的边长 [英] Finding side length of a cross-section of a pyramid frustum/truncated pyramid

问题描述

如何求横截面的边长(如图所示)下图 - 横截面红色)的锥台/截棱锥?

How do I find the side length of a cross-section (as illustrated in the drawing below - cross-section in red) of a pyramid frustum/truncated pyramid?

我知道顶部和底部的边长，底部的高度截锥体和到横截面的距离.此外我知道顶部和底部底部平行，顶部和底部的中心底部底座直接位于彼此的顶部.

I know the side-lengths of the top and bottom base, the height of the frustum and the distance to the cross-section. Furthermore I know the top and bottom base are parallel and that the center of the top and bottom base are directly on top of each other.

推荐答案

比例是线性的，所以只需用切割高度占总高度的比例插入底边和顶边的长度即可.

The proportions are linear, so just interpolate the lengths of the bottom and top sides with the proportion of the cut height with the total height.

cut_side = (cut_height/total_height)*(bottom_side-top_side)+top_side

(无论如何，请仔细检查以确保 100% 确定).

(Anyway, double check it to be 100% sure).

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