Area of a linearly transformed curve

Let $C$ be a closed curve in the $xy$ plane, with an enclosed area of $A$ . The points on this curve are operated on by a linear transform, given by $\mathbf{y = T x}$ , where $\mathbf{x}$ is the vector representing any point on $C$ , and $\mathbf{y}$ is the vector of the its image, and matrix $T$ is given by

$T = \begin{bmatrix} 1 && 2 \\ 3 && 4 \end{bmatrix}$

What will be the area of the transformed curve?