a concave quadrilateral, one interior angle is bigger than 180°, and one of the two diagonals lies outside the quadrilateral. A dart (or arrowhead) is a concave quadrilateral with bilateral symmetry like a kite, but where one interior angle is reflex. See Kite. Complex quadrilaterals A self-intersecting quadrilateral is called variously a cross-quadrilateral, crossed quadrilateral, butterfly quadrilateral or bow-tie quadrilateral. In a crossed quadrilateral, the four "interior" angles on either side of the crossing (two acute and two reflex, all on the left or all on the right as the figure is traced out) add up to 720°. Crossed trapezoid (US) or trapezium (Commonwealth): a crossed quadrilateral in which one pair of nonadjacent sides is parallel (like a trapezoid) Antiparallelogram: a crossed quadrilateral in which each pair of nonadjacent sides have equal lengths (like a parallelogram) Crossed rectangle: an antiparallelogram whose sides are two opposite sides and the two diagonals of a rectangle, hence having one pair of parallel opposite sides Crossed square: a special case of a crossed rectangle where two of the sides intersect at right angles Special line segments The two diagonals of a convex quadrilateral are the line segments that connect opposite vertices. The two bimedians of a convex quadrilateral are the line segments that connect the midpoints of opposite sides. They intersect at the "vertex centroid" of the quadrilateral (see below). The four maltitudes of a convex quadrilateral are the perpendiculars to a side—through the midpoint of the opposite side. Area of a convex quadrilateral There are various general formulas for the area of a convex quadrilateral ABCD with sides . Trigonometric formulas The area can be expressed in trigonometric terms as where the lengths of the diagonals are and and the angle between them is . In the case of an orthodiagonal quadrilateral (e.g. rhombus, square, and kite), this formula reduces to since is . The area can be also expressed in terms of bimedians as where the lengths of the bimedians are and and the angle between them is . Bretschneider's formula expresses the area in terms of the sides and two opposite angles: where the sides in sequence are , , , , where is the semiperimeter, and and are two (in fact, any two) opposite angles. This reduces to Brahmagupta's formula for the area of a cyclic quadrilateral—when . Another area formula in terms of the sides and angles, with angle