If the quadrangle is a square or rectangle: Area = length × width
If the quadrangle is a parallelogram: Area = base × height
If the quadrangle is a trapezoid: Area = 1/2 × (sum of parallel sides) × height
If the quadrangle is a kite or rhombus: Area = 1/2 × diagonal 1 × diagonal 2
If the quadrangle is irregular: split it into triangles, find each triangle’s area, then add them
If the four sides and one diagonal are known: use the diagonal to divide it into two triangles and apply Heron’s formula to each triangle
If the coordinates of the vertices are known: use the shoelace formula
If only side lengths and angles are known: use trigonometric area formulas or divide into triangles