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We have a trapezoid and we know radiuses of its escribed circles. Now we want to calculate area of this trapezoid with radiuses. Radiuses of two circles that are besides the legs of trapezoid (and between parallel sides) is the same.(r1=r2) And height of trapezoid equal with diameter of these circles.(h=2r1=2r2) Now we have height and one more thing that we need is lengths of the parallel sides. And I don't have any idea how find those.

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  • $\begingroup$ I don't know what a trapezoid with radius is. Can you give a picture example, or describe it better? $\endgroup$ – Calvin Khor Jan 9 at 9:16
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Excircles radii are not enough to compute the area of the trapezoid, as you can see from the animation below: excircles have always radii $1$, $1$, $1$ and $3$, but the area of the trapezoid varies.

enter image description here

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