Ellipsoid surface area
JavaScript (ES7),  86 83  82 bytes
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An approximation of Thomsen's approximation.

(a,b,c)=&gt;(519*((a*b)**(p=1.535)+c**p*(b**p+a**p))/(31+27*a*b*c/(a+b+c)**3))**(1/p)

Try it online!