In the adjoining figure, ABCD is a quadrilateral. If the diagonal of a quadrilateral is BD (d), perpendiculars are drawn from vertices A and C to the diagonal BD. Therefore,
Height of ΔABD (AF) = h₁ and height of ΔCBD (CE) = h₂.
Now,
Area of quadrilateral ABCD (A) = Area of ΔABD + Area of ΔCBD
= ½ BD × AF + ½ BD × CE
= ½ BD × (AF + CE)
= ½ × d × (h₁ + h₂)
Hence,
Area of quadrilateral (A) = ½ × d × (h₁ + h₂)
= ½ × diagonal × Sum of the perpendiculars drawn on the diagonal.