A regular hexagon is inscribed in a circle. If the area of the hexagon is 24root3 cm2 find the area of the circle
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Dividing a hexagon into 6 equal parts gives 6 triangles with angle at center being 360/6 = 60 degrees.
Area of hexagon = 6 x area of each triangle
Area of triangle = 1/2 ab Sinβ (where β = angle between the sides)
'a' and 'b' are both = 'r' = the radius of the circle
Area of hexagon = 6 x 1/2 x r x r x Sin 60 = 24√3
r² = 16
r = 4 cm
Area of circle = 22/7 x 4² = 50.29 cm²
Area of hexagon = 6 x area of each triangle
Area of triangle = 1/2 ab Sinβ (where β = angle between the sides)
'a' and 'b' are both = 'r' = the radius of the circle
Area of hexagon = 6 x 1/2 x r x r x Sin 60 = 24√3
r² = 16
r = 4 cm
Area of circle = 22/7 x 4² = 50.29 cm²
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Answer:
Step-by-step explanation:
Join all corners of hexagon with centre of cirlce and u will see 6 equilateral traingles there!!
Let the radius of circle be "r" which is same as side of equilateral traingles!!
Since there are 6 equilateral triangle forming that hexagon!
6×[(root3)/4]a.a=24root3
a=4
Area of circle = πa.a
=16π
=16×3.14
=50.24 cm^2
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