If Γ is a closed Jordan curve that encloses a region with area A, show that $A=\frac{1}{2i} \int_{\Gamma} \overline{z}dz$.

Question

If Γ is a closed Jordan curve that encloses a region with area A, show that $A=\frac{1}{2i} \int_{\Gamma} \overline{z}dz$. Then show that $A=\frac{1}{2i} \int_{\Gamma} \overline{z}dz$ can be written as $A=\frac{1}{4i}\int_{\Gamma}\overline{z}-z d\overline{z}$.

I have no clue where to start here.