Question

Find the area of the following fields. All dimensions are in metres.

Answer 1

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