Find the area of the field shown along side. All dimension are in metres

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Solution

Area of $A B C D E =$ Area of $△ A B H +$ area of trap $B C F H +$ area of $△ C D F +$ Area of $△ A E D$
Now, area of $A B H$
$= \times A H \times H B$
$= \frac{1}{2} \times 25 \times 25$
$= \frac{625}{2} m^{2} = 312.5 m^{2}$
Area of trap $B C F H = \frac{1}{2} \times (H B + F C) \times H F$
$= \frac{1}{2} (25 + 50) \times 55 m^{2}$
$= \frac{75 \times 55}{2} m^{2} = 2062.5 m^{2}$
Area of $△ C D F = \times F C \times D F$
$= \frac{1}{2} \times 50 \times 50 m^{2} = 1250 m^{2}$
Area of $△ A E D = \times A D \times E G$
$= \frac{1}{2} \times 130 \times 60$
$= 3900 m^{2}$
Thus, area of $A B C D E = 312.5 m^{2} + 2062.5 m^{2} + 1250 m^{2} + 3900 m^{2}$
$= 7525 m^{2}$

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