The maximum area is a square. If the square has side x, its perimeter is 4x metres. So the cost of the fencing is 30*4x=$120x. When we add in the sales tax we have 120x*1.13=7000. So x=7000/(120*1.13)=7000/135.6=51.62m. This gives an area of 2,664.87 sq m.
To prove that a square gives the maximum area for a given length of fencing, let the length be x-y and the width be x+y. The perimeter is 2(x-y+x+y)=4x and the area x^2-y^2. This area is maximum when y=0, so the length and width are the same, so we have a square.