Finally, note that trapezoidal triples are close cousins of Pythagorean triples: if $p^2+q^2=r^2$, then $(q+p)^2+(q-p)^2=2r^2$ so that the Pythagorean triple $(p,q,r)$ corresponds to the trapezoidal triple $(q+p,r,q-p)$. If reconstructions of the damaged number at the top of the tablet are to be believed, IM 58045 from the Old Akkadian period (2400 BCE–2250 BCE) may provide an even older example of this triple and is, in fact, one of the oldest known mathematical tablets. The triple $(51,39,21)$ that appears on VAT 8512 is a multiple of the latter. Two whole-number "trapezoidal triples" $(a,ja,ka)$ are $(7,5,1)$ and $(17,13,7)$. An isosceles trapezoid has the area of 1500 cm has the height of 30 cm. Problems given in Old Babylonian scribal education were generally contrived so as to have exact, finite representations in base-60 notation. As an example, it was used in the breathtakingly elegant solution to the problem on cuneiform tablet VAT 8512, which is explained in Jens Høyrup's book Algebra in Cuneiform: Introduction to an Old Babylonian Geometrical Technique. Historical aside: The key fact was known in Old Babylonian times (~2000 BCE– ~1600 BCE). The important thing is to note that $(a-ka)=\frac , I suggested it as an edit to his, but the edit was rejected. Reflecting isosceles trapezoid ABCE across FE preserves it, making FE a line of symmetry.This builds on Ross Milkman's answer and makes it more explicit. In the figure above, altitude FE bisects bases AD and BC.
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