An agriculture field has a shape of an irregular polygon as shown in the figure. It's dimensions are given. Calculate it's area.
Given: $A B = 220 m, A L = 20 m, A M = 30 m, B N = 160 m, O B = 40 m, T M = O S = 60 m, L P = 20 m, N Q = 60 m, M N = 30 m$

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Solution

To find the area of the field we need to find the sum of area of its parts.
Area of $△ A L P = \frac{1}{2} \times A L \times L P$
$= \frac{1}{2} \times 20 \times 20 = 200 m^{2}$
Area of trapezium $P L N Q = \frac{1}{2} \times L N \times (L P + N Q)$
$= \frac{1}{2} \times 40 \times (20 + 60)$
$= \frac{1}{2} \times 40 \times 80 = 1600 m^{2}$
Area of ractangle $Q N B R = B N \times N Q = 160 \times 60 = 9600 m^{2}$
Area of $△ A M T = \frac{1}{2} \times A M \times M T = \frac{1}{2} \times 30 \times 60 = 900 m^{2}$
Area of rectangle $T M O S = T M \times O M = 60 \times 150 = 9000 m^{2}$
Area of $△ S O B = \frac{1}{2} \times O S \times O B = \frac{1}{2} \times 60 \times 80 = 1200 m^{2}$
$∴$ Area of the field $= 200 + 1600 + 9600 + 900 + 9000 + 1200 = 22, 500 m^{2}$

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