Question

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

Answer 1

ANSWER:ar(quad ABCD) = ar$△ABD)+ar(△BDC$
= $\frac{1}{2}\times BD\times AL+12\times BD\times \times CM$
= $\frac{1}{2}\times BD\times (A+CM)$
Substituting the values, we have;
ar(quad ABCD) = ​ $\frac{1}{2}\times 14\times (8+6)$
= 7 ​⨯ 14
= 98 $c{m}^2$