Find the area of the hexagon ^@ABCDEF^@ in which each side measures ^@17 \space cm,^@ width ^@BD = 30 \space cm,^@ and height ^@CF = 33 \space cm.^@
    C A B E D D 33 cm F 30 cm 17 cm


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Answer:

^@750 \space cm^2^@

Step by Step Explanation:
  1. Let us join ^@CF^@ and draw ^@AL \perp CF.^@
      C A B E D D 33 cm F 30 cm 17 cm L 15 cm
    Now, ^@AL = \dfrac { BD }{ 2 } = \dfrac { 30 }{ 2 } = 15 \space cm^@
  2. Area of hexagon ^@ABCDEF = ^@ Area of trapezium ^@ABCF^@ + Area of trapezium ^@CDEF^@ @^\begin{align} &= 2 \times \text { Area of trapezium ABCF } && \text{[Area of both the trapeziums will be same.]}\\ &= 2 \times \dfrac {1}{2}(AB + CF) \times AL \\ &= (17 + 33) \times 15 \space cm^2 \\ &= 750 \space cm^2 \end{align}@^

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