Symplectic Area vs. the area of a Riemannian parallelogram.

Question

Given two vectors $u,v\in\mathbb{R}^2$ and a Symplectic form $\omega$ with compatible inner product $g$, define the Symplectic area of $u,v$ as $\omega(u,v)$ and the Riemannian area to be the area of the parallelogram spanned by $u$ and $v$. The problem is to show that the Symplectic area is less that or equal to the Riemannian area for any two vectors in $\mathbb{R}^2$. I feel like there is some simple trick that makes this inequality trivial but it is escaping me. Any hints would be much appreciated.