AMO 2021 – Junior College (Grades 11–12) Question 23

In $\triangle PQR$, $PR=6$ cm, $QR=8$ cm and $PQ=10$ cm. Points $A,B$ lie on $PR$, points $C,D$ lie on $QR$, and $E$ is the midpoint of $PQ$. Given $PA=RB=RC=QD=2$ cm, find the area of pentagon $ABCDE$ in square centimetres.