How to prove that infinite number of pentagons exist satisfying the given requirements A given convex pentagon ABCDE has the property that the area of each of the 5 triangles ABC, BCD, CDE, DEA and EAB are equal. How can I prove that there exist infinitely many non-congruent pentagons having the above property? I tried to take one side of the triangle as fixed and build upon it but I couldn't do anything as I couldn't determine the angle of the pentagon. Any help please

The regular pentagon has this property. Any invertible affine transformation
of the plane has the property that equal areas are sent to equal areas. So
for instance we can stretch the regular pentagon by a given scale factor in the
$x$-direction (but leave the scale in the $y$-direction unchanged) to get an infinite family of non-congruent pentagons with your area property.
