If the quadrilateral is a rectangle: Area = length × width
If the quadrilateral is a square: Area = side × side
If the quadrilateral is a parallelogram: Area = base × height
If the quadrilateral is a trapezoid: Area = 1/2 × (sum of parallel sides) × height
If the quadrilateral is a kite: Area = 1/2 × diagonal1 × diagonal2
If the quadrilateral is cyclic: Area = √[(s−a)(s−b)(s−c)(s−d)], where s = (a+b+c+d)/2
If the quadrilateral is irregular: divide it into triangles and add the triangle areas
If the coordinates of the vertices are known: use the shoelace formula
If one diagonal is known and the two triangles formed are known: add the areas of both triangles