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Answer:
Area of the shaded region
= area (Δ ABC) - area (Δ DBC).
For Δ ABC having sides 122 m, 120 m and 22 m, we have
s=12(122+120+22)m
=(12×264)m=132m.
∴ (s−a)=(132−122)m=10m,
(s−b)=(132−120)m=12m
and (s−c)=(132−22)m=110m.
∴ area(ΔABC)=s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√
=132×10×12×110−−−−−−−−−−−−−−−−√m2
=(12×11×10)m2=1320m2.
For Δ DBC having sides 26 m, 24 m and 22 m, we have
s=12(26+24+22)m=(12×72)m=36m.
∴ (s−a)=(36−26)m=10m,(s−b)=(36−24)m=12mand(s−c)=(36−22)m=14m.
∴ area(ΔDBC)=s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√
=36×10×12×14−−−−−−−−−−−−−−−√m2
=24×105−−−√m2=(24×10.25)m2 (approx).
=246m2.
∴ area of the shaded region
= area(ΔABC)-area(ΔDBC)
=(1320−246)m2=1074m2.
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Author:
teresaanthony
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