Find the area of quadrilateral whose one diagonal is 20 cm long and the perpendiculars to this diagonal from other vertices are of length 9 cm and 15 cm.

Consider ABCD as a quadrilateral in which BD = 20 cm, AY = 15 cm and CX = 9 cm.

Area of quadrilateral ABCD = Area of triangle ABD + Area of triangle BCD

Area of triangle = $\dfrac{1}{2}$ × base × height

∴ Area of quadrilateral ABCD = $\dfrac{1}{2}$ × BD × AY + $\dfrac{1}{2}$ × BD × CX

Substituting the values we get,

Area of quadrilateral ABCD = $\dfrac{1}{2}$ x BD x (AY + CX)

= $\dfrac{1}{2}$ x 20 x (15 + 9)

= 10 x 24

= 240 cm²

Hence, area of quadrilateral = 240 cm².