Question

In the adjoining figure, ABCD is a quadrilateral in which diagonal BD = 14 cm. If AL ⊥ BD and CM ⊥ BD such that AL = 8 cm and CM = 6 cm, find the area of quad. ABCD.

Answer 1

ar(quad ABCD) = ar(∆ABD) + ar(∆BDC)
= $\frac{1}{2}$ ⨯ BD ⨯​ AL + $\frac{1}{2}$ ⨯ BD ⨯ CM
= $\frac{1}{2}$⨯ BD ⨯​ (AL + CM)
By substituting the values, we have:
ar(quad ABCD) = $\frac{1}{2}$⨯ 14 ⨯ (8 + 6)
= 7 ​⨯14
= 98 cm²
∴ Area of quad. ABCD = 98 cm²