  We prove two weighted geometric inequalities that hold for strictly mean
convex and star-shaped hypersurfaces in Euclidean space. The first one involves
the weighted area and the area of the hypersurface and also the volume of the
region enclosed by the hypersurface. The second one involves the total weighted
mean curvature and the area of the hypersurface. Versions of the first
inequality for the sphere and for the adS-Reissner-Nordstr\"om manifold are
proven. We end with an example of a convex surface for which the ratio between
the polar moment of inertia and the square of the area is less than that of the
round sphere.
