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Motivated by the relationship between the area of the image of the unit disk under a holomorphic mapping $h$ and that of $zh$, we study various $L^2$ norms for $T_{\varphi }\left(h\right)$, where $T_{\varphi }$ is the Toeplitz operator with symbol $\varphi$. In Theorem , given polynomials $p$ and $q$ we find a symbol $\varphi$ such that $T_{\varphi }\left(p\right)=q$. We extend some of our results to the polydisc.