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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 ΔEFH + Area of rectangle EDCI + Area of trapezium FHJG + Area of trapezium ICBK + Area of ΔGJA + Area of ΔKBA
Area of ΔEFH = `1/2 xx "Base" xx "Height"`
= `1/2 xx 40 xx 80`
= 40 × 40
= 1600 m2
Area of rectangle EDCI = Length × Breadth = 100 × 160 = 16000 m2
Area of trapezium FHJG = `1/2` × [Sum of parallel sides] × Height
= `1/2 xx [40 + 160] xx 160`
= `200/2 xx 160`
= 100 × 160
= 16000 m2
Area of trapezium ICBK = `1/2` × [Sum of parallel sides] × Height
= `1/2 xx [60 + 100] xx 120`
= `1/2 xx 160 xx 120`
= 80 × 120
= 9600 m2
Area of ΔAJG = `1/2` × Base × Height
= `1/2 xx 160 xx 100`
= 80 × 100
= 8000 m2
Area of ΔKBA = `1/2` × Base × Height
= `1/2 xx 60 xx 60`
= 60 × 30
= 1800 m2
Thus, the area of the complete figure
= 1600 + 16000 + 16000 + 9600 + 8000 + 1800
= 53000 m2
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