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Area of Polygons

Find the area...

Question

Find the area of polygon $A B C D E F$ if $A L = 80 m, A M = 100 m, A N = 160 m, A B = 240 m$
$C L = 50 m, D N = 60 m, A F = 30 m, E M = 40 m$ .

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Solution

$\begin{matrix} B N = A B - A N = 240 - 160 = 80 m M B = A N - A M = 160 - 100 = 60 m L N = A N - A L = 160 - 80 = 80 m a r e a o f p o l y g o n A B C D E F = a r e a o f Δ A L C + a r e a o f Δ D B N + a r e a o f Δ B E M + a r e a o f t r a p e z i u m (C D N L) + a r e a o f t r a p e z i u m (A M E F) \Rightarrow \frac{1}{2} \times A L \times C L + \frac{1}{2} \times B N \times D N + \frac{1}{2} \times E M \times M B + \frac{1}{2} \times (C L + D N) \times L N + \frac{1}{2} \times A F + E M \times A M \frac{1}{2} \times 80 \times 50 + \frac{1}{2} \times 80 \times 60 + \frac{1}{2} \times 40 \times 60 + \frac{1}{2} \times (50 + 60) \times 80 + \frac{1}{2} \times (30 + 40) \times 100 \Rightarrow 2000 + 2400 + 1200 + 4400 + 3500 \Rightarrow 13, 500 m^{2} \end{matrix}$

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