Math Arguments

Is it always possible?

TickTockMaths thinks this is the worst problem ever because a student could find the area by adding the sides together.




Consider the named shapes of irregular or regular polygons such as:
triangle
quadrilateral
-- dart, kite, rhombus, square, trapezoid, etc.
pentagon
hexagon
etcetera.

Is it always possible to find a size for which the area and perimeter are equal?

For which shapes can we find integer solutions?