Here, c^2=a^2+b^2 indicates that it is a right angled triangle that means angle C=90degree

and 4s(s-a)(s-b)(s-c)=4(area of triangle)^2   as area of triangle= √s(s-a)(s-b)(s-c)

also area of triangle = 1/2abcosC

2(area of triangle)=ab (cosC=cos90=1)

by squaring on both sides we get

4(area of triangle)^2=a^2b^2 

and thats the required answer.