An almost nonexistent Triangle

Geometry Level pending

Find the area of a triangle for which the side lengths, \(a, b\) and \(c\) are \(15, 11\) and \(\dfrac{77}{3}\), respectively.

If this area is of the form \(\dfrac{r}{s}\sqrt{kmn}\), where \(r\) and \(s\) are relatively prime and \(k,m\) and \(n\) are distinct prime numbers, evaluate \(r+s+k+m+n.\)

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