Irregular Convex Quadrilateral
Quadrilateral description

Side a
Side b
Side c
Side d
Diagonal AC (p)
Diagonal BD (q)
Angle α
Angle β
Angle γ
Angle δ
Quadrilateral area
Quadrilateral perimeter
Angle between diagonals

Area of triangle ABC
Area of triangle ACD
Area of triangle ABD
Area of triangle BCD
    Degree   Radian    
Input Limit:

Four sides of an irregular quadrilateral can be arranged in convex, concave or crossed shape.

Quadrilateral forms

(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:

Quadrilateral area
It can be seen from Fig. 3 that folding triangle BCD along q axis forms a concave quadrilateral.
The quession 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 trianglr BCD instead.