Question

Look at the measures shown in the adjacent figure and find the area of $PQRS$.

Answer 1

In $△PRS$

$PR=\sqrt{{PS}^2+{SR}^2}=\sqrt{{36}^2+{15}^2}$

$PR=3\sqrt{{12}^2+5^2}=39m$

$Ar\left(△PSR\right)=\frac{1}{2}\times PS\times SR=\frac{1}{2}\times 15\times 36=270㎡$

$Ar\left(△PQR\right)$

by using heron's formula,

Let $a=56,b=25,c=39$

So, $S=\frac{a+b+c}{2}=60$

$Ar△PQR=\sqrt{s\times (s-a)\times (s-b)\times (s-c)}$

$Ar\left(△PQR\right)=\sqrt{60\times 4\times 35\times 21}=420㎡$

So, $Ar\left(PQRS\right)=Ar\left(△PQR\right)+Ar\left(△PRS\right)=420+270$

$Ar\left(PQRS\right)=690㎡$