Question

In the figure given, $ABCD$ is a quadrilateral with $AB$ parallel to $DC$ and $AD$ parallel to $BC.ADC$ is a right angle. If the perimeter of the triangle $ABE$ is $6$ units, what is the area of the quadrilateral?

• A. $2\sqrt{3}$ square units
• B. $4$ square units
• C. $3$ square units
• D. $4\sqrt{3}$ square units

Answer 1

The correct option is A $2\sqrt{3}$ square units

Area of the triangle $ABE$ is half the area of the quadrilateral $ABCD$.
$△ABE$ is an equilateral triangle with perimeter $6$ units; so the side is $2$ units.
Area of $△ABE=\frac{\sqrt{3}}{4}\times 2^2$ sq. units $=\sqrt{3}$ sq. units
Therefore, area of the quadrilateral $ABCD=2\sqrt{3}$ sq. units.