An equidiagonal quadrilateral is a convex quadrilateral whose diagonals have equal lengths. Examples include isosceles trapezoids, rectangles, and squares (Josefsson 2014, p. 129).
A convex quadrilateral is equidiagonal iff its Varignon parallelogram is a rhombus, or equivalently iff its bimedians are perpendicular (Josefsson 2014, p. 131). Thus its area is
 |
where 
and 
are the lengths of the bimedians.
If 
is the common polygon diagonal length
and 
is the angle between the diagonals,
then
 |
An equidiagonal quadrilateral with perpendicular diagonals is a midsquare quadrilateral.
