Question

Question 16

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

(a) $72c{m}^2$ (b) $36c{m}^2$ (c) $24c{m}^2$ (d) $18c{m}^2$

Answer 1

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 $ABCD=2\times Areaof\Delta ABC$
$=2\times 18$
$=36c{m}^2$