In the given figure, ABCD is a quadrilateral in which diagonal BD = 24 cm, AL ⊥ BD and CM ⊥BD such that AL = 9 cm and CM = 12 cm. Calculate the area of the quadrilateral.

Question

In the given figure, ABCD is a quadrilateral in which diagonal BD = 24 cm, AL ⊥ BD and CM ⊥ BD such that AL = 9 cm and CM = 12 cm. Calculate the area of the quadrilateral.

Philoid · Accepted Answer

Given:

BD = 24 cm

AL = 9 cm

CM = 12 cm

In ∆ADB,

Area of ∆ADB = 1/2 × BD × AL

= 1/2 × 24 cm × 9 cm

= 108 cm²

In ∆CDB,

Area of ∆CDB = 1/2 × BD × CM

= 1/2 × 24 cm × 12 cm

= 144 cm²

Now,

Area of quadrilateral ABCD = Area of ∆ADB + Area of ∆ADB

= 108 cm² + 144 cm²

= 252 cm²