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Answer:
the area of shaded region = 1074 m2
Step-by-step explanation:
in big triangle
s = (120+122+22 )m÷ 2
s = 264m ÷ 2
s = 132m
area of big ∆=√132×132-120×132-122×132-22
= √ 132×12×10×110
(we factor this no. 132,12,10,110)
= √ 2×2×3×11 ×2×2×3 ×2×5 ×2×5×11
= 2×2×2×3×5×11
= 1320 m2
now, in small triangle
s = (24+26+22) m ÷ 2
s= 72m ÷2
s= 36m
area of small∆ = √ 36×36-24×36-26×36-22
= √ 36×12×10×14
(we factor this no. 36,12,10,14)
= √ 2×2×3×3×2×2×3×2×5×2×7
= 2×2×2×3√3×5×7
= 24 √ 105 m2
= 24× 10.25 m2
= 246 m2
now, the area of shaded region =
( area of big triangle - area of small triangle)
= (1320-246) m2
= 1074 m2 ans.