Area of Quadrilateral

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.

Area of quadrilateral ABCD (A) = Area of △ABD + Area of △CBD
=
12 BD × AF + 12 BD × CE
=
12 BD × (AF + CE)
=
12 d × (h₁ + h₂)
Hence,
Area of quadrilateral = 12 d × (h₁ + h₂)
=
12 × diagonal × sum of perpendiculars