Area of a General Quadrilateral

Q. From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 14 cm, 10 cm, and 6 cm.
The area of the triangle is $300\sqrt{m}c{m}^2$ where $m$ is _______

Q. Length $=4.5cm$, breadth $=2cm$.

Q. In a pentagon $ABCDE$, $DP$ is drawn perpendicular to $AB$ and is perpendicular to $CE$ also at point $Q$. If $AP=BP=12$ cm, $EQ=CQ=8$ cm, $DE=DC=10$ cm and $DP=18$ cm, find the area of the pentagon $ABCDE$.

1. $288$ sq. cm
2. $280$ sq. cm
3. $188$ sq. cm
4. $168$ sq. cm