If $\text{Area} (A) = \text{Area} (B)$ and $\text{Perimeter}(A) = \text{Perimeter}(B) \implies A \cong B$? If I have an $n$-gon $A$ and a convex $n$-gon $B$ with the same  perimeter and the same area, does $A\cong B$?
Edit : What becomes the answer if I replace convex by regular?

If they're both regular then just one of the given equalities is enough to show they're congruent.

For example, let's denote $a_1, a_2$ the edges of the two equal perimiter polygons, then we get $na_1=na_2$. Clearly $a_1=a_2$. Same goes for area.
