Question

In the diagram $\Delta ABC$ is right angled at $C$. Also $M,N$ and $P$ are the mid points of sides $BC,AC$ and $AB$ respectively. If the area of $\Delta APN$ is $2$ sq cm, then the area of $\Delta ABC$ in sq cm is:

• A. $8$ sq cm
• B. $12$ sq cm
• C. $16$ sq cm
• D. $4$ sq cm

Answer 1

The correct option is A $8$ sq cm

Ar. of triangle = $\frac{1}{2}\times Base\times Height$
Ar$\left(△APN\right)=\frac{1}{2}AN\times PN$
$2=\frac{1}{2}AN\times PN$
$AN\times PN=4$
$(2\times AN)(2\times PN)=16$
$AC\times BC=16$
$\frac{1}{2}AC\times BC=8$
$\Rightarrow Ar\left(△ABC\right)=8$ sq cm