Find the area of the octagon ^@ ABCDEFGH ^@ having each side equ | Math Question and Answer | Edugain Philippines

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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:

$1311 \space cm^2$

Step by Step Explanation:

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

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