Question

Calculate the area of $\Delta PQR$ where $OP=6cm,OR=8cm$ and $QR=26cm.$

Answer 1

$\Delta PQR$ is right Angled $\Delta$ with $\angle POR={90}^{\circ }$

$\therefore \sqrt{(PO{)}^2+(OR{)}^2}=PR$

$\Rightarrow PR=\sqrt{6^2+8^2}=\sqrt{100}$

$=10cm$

and

$\Delta$ PQR is right Angled $\Delta$ with

$\angle QPR={90}^{\circ }$

$\therefore (PQ{)}^2+(PR{)}^2=(QR{)}^2$

$\Rightarrow PQ=\sqrt{(26{)}^2-(10{)}^2}$

$=\sqrt{676-100}$

$=\sqrt{576}$

$24cm$

$\therefore$

Ar of $\Delta PQR=\frac{1}{2}base\times height$

$=\frac{1}{2}\times 10\times 24$

$=120c{m}^2$