Question

2. Find the area of the field ABCDEF, as shown below:

Answer 1

Heya
Here is your answer


In ∆ AFE,
base = 150cm
perpendicular height = 40cm
area = ½× base × height
= ½ × 150 × 40
= 3000cm² ......................................(i)


In rectangle ABDE,
length = 120cm
breadth = 150cm
area = lenght × breadth
= 120 × 150
= 18000cm² ...................................(ii)



In ∆ BCD,
let Sides = a = BC = 90cm
b = CD = 120cm
c = DB = 150cm
as perpendicular height is not given,
area = √[ s (s-a) (s-b) (s-c) ]

s = perimeter/2
= (90 + 120 + 150)/2
= 360/2
= 180cm

area = √ [ 180 (180-90) (180-120) (180-150) ]
= √[ 180 × 90 × 60 × 30 ]
= √[ (2 × 3 × 3 × 2 × 5) × (3 × 3 × 2 × 5) × (3 × 2 × 2 × 5) × (3 × 2 × 5) ]

as factors of 180 are 2×2×3×3×5
90 are 2×3×3×5
60 are 2×2×3×5
30 are 2×3×5

= √ [ 2×2×2×2×2×2×3×3×3×3×3×3×5×5×5×5]
= 2×2×2×3×3×3×5×5

{ Note : √(a×a) = a }

= 5400cm² ............................(iii)



area of ABCDE,
= area of ∆AEF + area of ABDE + area of ∆BCD
= equation (i) + (ii) + (iii)
= 3000 + 18000 + 54000
= 75000cm²



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Answer 2

$\huge\mathfrak\blue{ƛƝƧƜЄƦ:-}$

answer is 26,400 cm^2