Question

The figure ABCD is a quadrilateral in which AB is parallel and equal to CD and BC is parallel and equal to AD. Its area is

• A. $72c{m}^2$
• B. $36c{m}^2$
• C. $24c{m}^2$
• D. $64c{m}^2$

Answer 1

The correct option is B

$36c{m}^2$

It is clear from the figure that quadrilateral ABCD is a parallelogram. The diagonal AC of the given parallelogram ABCD divides it into two triangles of equal areas.
Area of the $\Delta ABC=\frac{1}{2}\times Base\times Height$
$=\frac{1}{2}\times 12\times 3=18c{m}^2$
$\therefore$ Area of the parallelogram $ABCD=2\times Areaof\Delta ABC$
$=2\times 18$ $=36c{m}^2$