Find the area of the shaded region in the given figure, where a circular arc of radius 6cm has been drawn with vertex O of an equilateral triangle OAB of side 10cm as centre.
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Answer:
Step-by-step explanation:
OAB is an equilateral Triangle with side 12 Circle with radius of 6
Each angle of an equilateral triangle is 60
o
Angle at the centre in segment θ=60
o
=Area of Major segment+Area of an equilateral triangle OAB
=(πr
2
− Area of Minor segment)+
4
3
×(12)
2
={πr
2
−
360
θ
×πr
2
}+36
3
={πr
2
−
360
60
×πr
2
}+36
3
={πr
2
−
6
1
×πr
2
}+36
3
=
6
5
×πr
2
+36
3
=
6
5
×
7
22
×(6)
2
+36
3
=
6
5
×
7
22
×36+36
3
={
7
660
+36
3
}cm
2
=94.28+36×1.73
=94.28+62.28
=156.56 sq.cm
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