Find the area of a quadrilateral whose diagonals are of length 18 cm and 12 cm and they intersect each other at right angles.

Consider ABCD as a quadrilateral in which the diagonals AC and BD intersect each other at M at right angles.

From figure,

AC = 18 cm and BD = 12 cm

When diagonals of a quadrilateral intersect at right angles,

Area of quadrilateral = $\dfrac{1}{2}$ x d₁ x d₂, where d₁ and d₂ are diagonals.

Substituting the values we get,

Area of quadrilateral ABCD = $\dfrac{1}{2}$ x 12 x 18

= 6 x 18

= 108 cm²

Hence, area of quadrilateral = 108 cm².