A regular hexagon is inscribed in a circle of radius 14 cm. Find the area of
the region between the circle and the hexagon. 22/7
Answers
The angle of regular hexagon is 120°. Thus the triangle formed AOD will be equilateral triangle and thier will be 6 such triangles each of side 7cm in the hexagon.
Area of hexagon = 6 x ar(eq. triangle)
= 6 x √3/4 x 7 x 7
= (147√3)/2 = 127.302 cm^2
Area of circle = π r^2
= 154 cm^2
Area required = ar(circle) - ar(hexagon)
= 154 - 127.302 = 26.698 cm^2
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Answer:
Explanation: side of the hexagon= 14 cm
A(Hexagon )= 6 × √3\4 × ( side)2
= 6×√3\4 ×14 ×14
= 6×0.433 ×196
= 509.208 cm2
A( circle) = πr`2
= 22\7 ×14×14
= 22\7×196
= 616 cm2
The area of region between the circle and hexagon
= A(circle)-A( hexagon)
= 616-509.208
= 106.792 cm2
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