Find the area of the hexagon ^@ABCDEF^@ in which each side measu | Math Question and Answer | Edugain South Africa

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Find the area of the hexagon $ABCDEF$ in which each side measures $17 \space cm,$ width $BD = 30 \space cm,$ and height $CF = 33 \space cm.$

Answer:

$750 \space cm^2$

Step by Step Explanation:

Let us join CF $C F$ $C F$ and draw AL⊥CF. $A L ⊥ C F .$ $A L ⊥ C F .$
Now, AL=BD2=302=15 cm $A L = \frac{B D}{2} = \frac{30}{2} = 15 c m$ $A L = \frac{B D}{2} = \frac{30}{2} = 15 c m$
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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