Question

In the adjoining figure, ABCD is a quadrilateral in which diag. 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