A midsquare quadrilateral is a convex quadrilateral whose diagonals are equal in length and perpendicular. It is therefore both an equidiagonal quadrilateral and an orthodiagonal quadrangle (Josefsson 2014, p. 137).
A convex quadrilateral is midsquare iff its Varignon
parallelogram is a square, or equivalently iff
its bimedians are equal in length
and perpendicular (Josefsson 2014, p. 137).
If 
is the common polygon diagonal length
and 
is the common bimedian length,
then its area is (Josefsson 2014, p. 138)
 |
A midsquare quadrilateral need not be a square. For example, the isosceles trapezoid with vertices 
,
,
,
and 
in boundary order has equal perpendicular diagonals
of length 
. A midsquare quadrilateral is a square iff its diagonals bisect
each other (Josefsson 2014, p. 138).
