Irregular convex quadrilateral calculator ▲  Side a
Side b
Side c
Side d
Diagonal AC (p)
Diagonal BD (q)
Angle α
Angle β
Angle γ
Angle δ
Angle between diagonals

Area of triangle ABC
Area of triangle ACD
Area of triangle ABD
Area of triangle BCD
 α1 α2 β1 β2 γ1 γ2 δ1 δ2
 Irregular convex quadrilateral summary ▲

Four sides of an irregular quadrilateral can be arranged in convex, concave or crossed shape. (We assume that the vertices are connected by the sequence from A to B then to C and to D and finally back to A) Because any arbitrary 4 sides can form a convex, concave or crossed quadrilateral it is mandatory to define the exact form.

In order to draw a quadrilateral closed shape the following inequalities must be fulfilled:

 a + b + c > d b + c + d > a c + d + a > b d + a + b > c

Any quadrilateral shape can be divided into 2 triangles.

The area of a convex quadrilateral can be expressed in one of the following formulas:  It can be seen from Fig. 3 that folding triangle BCD along q axis forms a concave quadrilateral. The question now is how can we estimate if folding the triangle will form a concave or crossed shape. From fig. 2 we can see that if β1> β2 and δ1> δ2 are both true then the new shape will be concave else if one of the criteria is false the new shape is a crossed quadrilateral. If both criteria are false then it is a concave shape but triangle ABD is folded into triangle BCD instead.