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Question
Find the area of the following fields. All dimensions are in metres.
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Solution
Area of the given figure
= Area of ΔDCF + Area of ΔEGD + Area of trapezium FCBH + Area of ΔEGA + Area of ΔAHB
∴ Area of ΔDCF = `1/2` × Base × Height
= `1/2 xx 100 xx 100`
= `10000/2`
= 5000 m2
Area of ΔEGD = `1/2` × Base × Height
= `1/2 xx 120 xx 180`
= 60 × 180
= 10800 m2
Area of trapezium = `1/2` × [Sum of parallel sides] × Height
= `1/2 xx [100 + 50] xx 110`
= `1/2 xx 150 xx 110`
= 75 × 110
= 8250 m2
Area of ΔEGA = `1/2` × Base × Height
= `1/2 xx 120 xx 80`
= 60 × 80
= 4800 m2
Area of ΔAHB = `1/2` × Base × Height
= `1/2 xx 50 xx 50`
= 25 × 50
= 1250 m2
Thus, the area of the complete figure
= 5000 + 10800 + 8250 + 4800 + 1250
= 30100 m2
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