Prove that for any quadrilateral with diagonals perpendicular, the area is half the product of the diagonals.

For this we choose a quadrilateral as shown below:

Clearly, diagonals of the quadrilateral are AC and BD, which are

perpendicular to each other.

Sum of areas of triangles ABD and CBD

Area of quadrilateral =

=

=

OA+OC=AC

=

Now,

Since, DB × AC = product of diagonals

Therefore, Area of quadrilateral =

Hence proved.