Italy
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.^@
Answer:
^@1311 \space cm^2^@
- 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}@^
