Question

A theatre, in the shape of a quadrilateral ABCD, has $\angle C={90}^{\circ }$, $AB=9m,BC=12m,CD=5mandAD=8m$. If the total area of theatre is $90m^2$, then what will be the area of $△BAD?$

• A. $50m^2$
• B. $55m^2$
• C. $60m^2$
• D. $65m^2$

Answer 1

The correct option is C $60m^2$

ABCD is the theatre as shown in the figure.
$△DBC$ is right angled at C.
$\text{Area of}△DBC=\frac{1}{2}\times base\times height$
$=\frac{1}{2}\times 12\times 5$
$=30m^2$
Now,
$Areaoftheatre=areaof△DBC+areaof△BAD$
$\Rightarrow 90=30+areaof△BAD$
$\Rightarrow areaof△BAD=60m^2$