In the adjoining figure ABC is an equilateral triangle and C is the centre of the circle. A and B lie on the circle. What is the area of the shaded region, if the diameter of the circle is 28 cm.
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30cm is the radiusvyv
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If the diameter of the circle is 28 cms, then its radius in 14 cms
i.e AC = BC = 14 cms
As Triangle ABC is an equilateral triangle, Angle ABC = BAC = ACB = 60 degrees = 1.0472 radians
Area of sector ABC = (1/2) * r^2 * angle of sector in radians
=(1/2) * (14^2) * 1.0472
= 102.6256
Area of equilateral triangle = (root(3))*(side)^2/4
= (root(3) * 14^2)/4
= 84.8704
Area of shaded area
= Area of sector - Area of triangle
=102.6256 - 84.8704
= 17.755
r = radius of circle
i.e AC = BC = 14 cms
As Triangle ABC is an equilateral triangle, Angle ABC = BAC = ACB = 60 degrees = 1.0472 radians
Area of sector ABC = (1/2) * r^2 * angle of sector in radians
=(1/2) * (14^2) * 1.0472
= 102.6256
Area of equilateral triangle = (root(3))*(side)^2/4
= (root(3) * 14^2)/4
= 84.8704
Area of shaded area
= Area of sector - Area of triangle
=102.6256 - 84.8704
= 17.755
r = radius of circle
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