Solve for C

A^2= 1/2(s-a)(s-b)(s-c)

OK  

multiply both sides by 2

2A^2 = (s-a)(s-b)(s-c)

divide both sides by (s-a)(s-b)

[2A^2]/[(s-a)(s-b)]  = s-c

Add c to both sides and subtract the expression on the left side from both sides

c = s - [2A^2]/[(s-a)(s-b)]

We could get a common denominator here, but the final result would be a little messy...this is good enough !!!