Question

Find the area of the quadrilateral PQRS.

• A. 690 sq. m
• B. 710 sq. m
• C. 890 sq. m
• D. 970 sq. m

Answer 1

The correct option is A 690 sq. m

Area of quadrilateral PQRS = Area of $△PSR$ + Area of $△PQR△PSR$ is right angles triangle.
Hence, Area of $△PSR=\frac{1}{2}\times base\times height$
$=\frac{1}{2}\times 15\times 36=270m^2$

$P{R}^2=P{S}^2+S{R}^2$
$P{R}^2={36}^2+{15}^2={39}^2$
$PR=39$
The sides of $△PQR$ are 25, 39 and 56.
$s=120/2=60$
$s-a=60-25=35$
$s-b=60-39=21$
$s-c=60-56=4$
Area of a triangle $=sqrt(6\times (6-a)\times (s-b)\times (s-c\left)\right)$
$=sqrt(60+35+21+4)$
$=420$
Area of quadrilateral $PQRS=$Area of $△PSR+$ Area of $△PQR$
$=270+420$
$=690m^2$