Question 6
In the diagram below, $ABC$ is a triangle, where the angle bisectors of $\angle ABC$ and $\angle ACB$ intersect at point $P$. Let points $D$ and $E$ lie on sides $AB$ and $AC$, respectively, such that $DE$ passes through point $P$ and $\angle AED=\angle ABP$. If the areas of triangles $BDP$, $CEP$ and $BPC$ are equal to 18 cm², 36 cm² and 57 cm², respectively, then what is the area, in cm², of $ABC$?
