Find the length AB, OA and OB
Then Area = sqrt[s(s-a)(s-b)(s-c)], where s = (a+b+c)/2, a, b and c are the sides of the triangle AOB.
If the shortest distance from A to the line OB. is d, then
Area AOB = 1/2*d*OB.
Find OB. You have already calculated area AOB. Find d.