 Square lamina

A square lamina is a frame obtained by removing a concentric square hole from a larger square, with corresponding sides parallel. If their side lengths are $a>b>0$, the uniform border thickness is $t=(a-b)/2$ and the frame has areaFor positive integer sides $a,b$ with the same integer parity, $t$ is a positive integer, and a unit-grid frame contains exactly $4t(b+t)$ unit squares. For example, outer side five and inner side three give thickness one and sixteen unit squares. Concentricity alone would allow a rotated inner square; the parallel-side condition is what makes this a uniform lattice border.