Question

In the adjoining figure, ABCD is a parallelogram. If AB$=16cm,AE=8cm$ and $CF=10cm,$ find $AD$.

Answer 1

Area of parallelogram $=Base\times Altitude$

For $ABCD,$

$AE\perp DC$

$\therefore$ $AE$ is altitude, $DC$ is the base.

$\Rightarrow$ Area of a parallelogram $=Base\times Altitude$

$=DC\times AE$

$=AB\times AE$ [ Opposite sides of parallelogram are equal ]

$=16\times 8$ ------ ( 1 )

For $ABCD,$

$CF\perp AD$

$\therefore$ Area of parallelogram $=Base\times altitude$

$=AD\times CF$

$=AD\times 10$ ------ ( 2 )

From ( 1 ) and ( 2 ),

$\Rightarrow$ $16\times 8=AD\times 10$

$\Rightarrow$ $AD=\frac{16\times 8}{10}$

$\Rightarrow$ $AD=12.8cm$