Question

Find the area of the irregular polygon shaped fields given below.

Answer 1

Area of the field = Area of trapezium FBCH + Area of ∆DHC + Area of ∆EGD + Area of ∆EGA + Area of ∆BFA

Area of the triangle = `1/2 "bh sq. units"`

Area of the trapezium = `1/2 xx "h" xx ("a" + "b")  "sq. units"`

Area of the trapezium FBCH = `1/2 xx (10 + 8) xx (8 + 3)  "m"^2`

= 9 × 11 = 99 m² ...(1)

Area of the ∆DHC = `1/2 xx 8 xx 5  "m"^2`

= 20 m²  ...(2)

Area of ∆EGD = `1/2 xx 8 xx 15  "m"^2`

= 60 m²  ....(3)

Area of ∆EGA = `1/2 xx 8 xx (8 + 6)  "m"^2`

 = 4 × 14 m² 

= 56 m² 

Area of ∆BFA = `1/2 xx 3 xx 6  "m"^2` 

= 9 m² 

∴ Area of the field = 99 + 20 + 60 + 56 + 9 m²

= 244 m²

Area of the field = 244 m²