Question

Find the area of quadrilateral ABCD in which diagonal BD = 24 cm. AL ⊥ BD and CM ⊥ BD such that AL = 5 cm and CM = 8 cm.

Answer 1

Let ABCD be the given quadrilateral and let BD be the diagonal such that BD is of the length 24 cm.
Let AL ⊥ BD and CM ⊥ BD
Then, AL = 5 cm and CM = 8 cm
Area of the quadrilateral ABCD = (Area of ΔABD + Area of ΔCBD)
= $\left[\left(\frac{1}{2}\times BD\times AL\right)+\left(\frac{1}{2}\times BD\times CM\right)\right]$ sq. units
= $\left[\left(\frac{1}{2}\times 24\times 5\right)+\left(\frac{1}{2}\times 24\times 8\right)\right]$ cm²
= ( 60 + 96) cm² = 156 cm²

∴ Area of the given quadrilateral = 156 cm