Question

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

Answer 1

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