The (logarithmic) Mahler measure of a non-zero rational poly- nomial P in n variables is defined as the mean of log |P | restricted to the standard n-torus (Tn = {(x1,...,xn) ∈ (C∗)n : |xi| = 1,∀ 1 ≤ i ≤ n}). It has been related to special values of L-functions. In 2008, Pritsker defined a natural counterpart of the Mahler measure by replacing the normalized arclength measure on the standard n-torus by the normalized area mea- sure on the product of n open unit disks. In a recent joint work with Prof. Matilde Lal ́ın, we investigated some similarities and differences between the two, and evaluated the areal Mahler measure of some multivariable poly- nomials, which also yields special values of L-functions. In this talk, we will discuss another joint work with Lal ́ın on the evaluations of the Areal Mahler measure of certain polynomials under a power change of variables. Further, we will evaluate the areal Mahler measure of the family of poly- nomials x + y + k, for all k ∈ C, using the areal analogue of the Zeta Mahler measure, and methods involving random walk and hypergeometric differential equations. This is an ongoing joint work with Lal ́ın, Nair, and Ringeling.