Question

Find the area of the quadrilateral $ABCD$.

Here, $AC=22$ cm, $BM=3$ cm,$DN=3$ cm, and $BM\perp AC,DN\perp AC$

Answer 1

Now, $ar\left(ABCD\right)=ar\left(\Delta ABC\right)+ar\left(\Delta ACD\right)$

$=\frac{1}{2}\times AC\times BM+\frac{1}{2}\times AC\times DN$

$=\frac{1}{2}\times AC(BM+DN)$

$=\frac{1}{2}\times 22\times (3+3)$

$=11\times 6$

$=66c{m}^2$

$\therefore ar\left(ABCD\right)=66c{m}^2$