  The paper deals with amoebas of $k$-dimensional algebraic varieties in the
algebraic complex torus of dimension $n\geq 2k$. First, we show that the area
of complex algebraic curve amoebas is finite. Moreover, we give an estimate of
this area in the rational curve case in terms of the degree of the rational
parametrization coordinates. We also show that the volume of the amoeba of
$k$-dimensional algebraic variety in $(\mathbb{C}^*)^{n}$, with $n\geq 2k$, is
finite.
