Parallelogram
= Parallelogram
{wiki}
A parallelogram is the <convex set> with vertices $p,p+u,p+v,p+u+v$ for two linearly independent planar vectors $u,v$. Its opposite edges are parallel and its centre $p+(u+v)/2$ gives central symmetry. Its area is $|\det[u,v]|$, so an invertible linear map changes its area by the absolute value of that map's <determinant>. These facts make parallelograms convenient convex bodies for two-dimensional applications of the <Minkowski convex body theorem>.