# Can the length of any chord that is parallel to the bases of a trapezoid be found if the lengths of the two bases are known?

Given the length of the bases of a trapezoid, the median can be found by the formula (b1 + b2)/2. From this the median can be found of the two resultant trapezoids formed by the median and the bases, and ad infinitum. So, at least theoretically, the length of *any* chord that is parallel to the bases can be found. I wonder if there is anyone who has reduced this iterative process into a formula.

This seems more suited to a general math forum like "math stack exchange" than to Ask Sage.

The answer is simple though: the length of a parallel to the bases varies linearly with the height.

So the length is

`(1 - t) * b1 + t * b2`

at a fraction`t`

of the way from base 1 to base 2.See intercept theorem.