Area of General Quadrilateral

To find area of any general quadrilateral,

We split it into triangles and add their area parallelogram has opposites sides equal & parallel

For Quadrilateral ABCD

We join AC

So, we have two triangles - Δ ADC and Δ ABC

Let h ₁ be height from point D to AC 

   & h ₂ be height from point B to AC

So,

Area of Quadrilateral ABCD

  = Area of Δ ADC + Area of Δ ABC

  = 1/2 × AC × h ₁ + 1/2 × AC × h ₂

  = 1/2 × AC × (h ₁ + h ₂ )

  = 1/2 × d  (h ₁ + h ₂ )

where d = Length of Diagonal

Find area of quadrilateral ABCD

Given

Length of diagonal = d = 10 cm

Length of Perpendicular dropped on AC

         h ₁ = 5 cm

     & h ₂ = 3 cm

Now,

 Area of ABCD = d/2 (h ₁ + h ₂ )

   = 10/2 (5 + 3)

   = 10/2 × 8

     = 5 × 8

     = 40 cm ²

Area of quadrilateral = 40 cm ²