### Find the area of the octagon $ABCDEFGH$ having each side equal to $17 \space cm, CH = DG = 33 \space cm$ and $EL \perp DG$ such that $EL = 15 \space cm.$ A B E F C D H G L 15 cm 17 cm 33 cm

$1311 \space cm^2$
1. Area of the octagon $ABCDEFGH =$ Area of trapezium $DEFG +$ Area of trapezium $ABCH +$ Area of rectangle $CDGH$ \begin{align} &= 2 \times \text{ Area of trapezium } DEFG + \text{ Area of rectangle } CDGH \\ &= 2 \times \dfrac {1}{2} \times (EF + DG) \times EL + (CH \times CD) \\ &= (17 + 33) \times 15 + (33 \times 17) \space cm^2 \\ &= 750 + 561 \space cm^2 \\ &= 1311 \space cm^2 \end{align}