Question

If Figure, calculate the area of quadrilateral $ABCD$.

• A. $32$
• B. $33$
• C. $34$
• D. $35$
• E. $36$

Answer 1

The correct option is E $36$

Join $B$ and $D$,

Now triangle $ABD$ is right angled triangle with right angle at $A$.

Observe that triangle $BDC$ is also an right angled triangle with right angle at $D$.

Area of given quadrilateral is equal to the sum of area of triangle $ABD$ and area of triangle $BDC$.

$\Rightarrow \frac{1}{2}\times AB\times AD+\frac{1}{2}\times BD\times DC=\frac{1}{2}\times 4\times 3+\frac{1}{2}\times 5\times 12=6+30=36$