The diagonals of a quadrilateral intersect each other at right angles. If the lengths of these diagonals be 14 cm and 19 cm respectively, find the area of the quadrilateral.

A quadrilateral ABCD is shown in the figure below:

The diagonals AC and BD intersect at O and are perpendiculars (90°)

Given,

AC = 14 cm

BD = 19 cm

When the diagonals of a quadrilateral intersect at right angles, the formula of area is:

Area = $\dfrac{1}{2}$ × d₁ × d₂

where d₁ and d₂ are diagonals.

Area = $\dfrac{1}{2}$ × 14 × 19

= 7 × 19

= 133 cm².

Hence, area = 133 cm².