A wire of cross sectional area A, modulus of elasticity $$2 \times 10^{11} \text{ Nm}^{-2}$$ and length $$2 \text{ m}$$ is stretched between two vertical rigid supports. When a mass of $$2 \text{ kg}$$ is suspended at the middle it sags lower from its original position making angle $$\theta = \frac{1}{100}$$ radian on the points of support. The value of A is ___________ $$\times 10^{-4} \text{ m}^2$$ (consider $$x << L$$). (given : $$g = 10 \text{ m/s}^2$$)