Question

Prove that for any quadrilateral in which the diagonals are perpendicular to each other, the area is half the product of the lengths of the diagonals.

Answer 1

Let the given quadrilateral be ABCD with AC = d₁ units, BD = d₂ units.

Also, AC and BD are perpendicular to each other.

Area of ΔABD =

Area of ΔBCD =

Now, area of the quadrilateral ABCD = Area of ΔABD + Area of ΔBCD

Hence, we can say that for any quadrilateral in which the diagonals are perpendiculars to each other, the area is half the product of the lengths of the diagonals.