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Math Help - finding areas perimeters and segments in circle

  1. #1
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    finding areas perimeters and segments in circle

    Hi, i really need help on working this one out as it is very important for school, thanks in advance.

    A circle has centre o and radius 1cm, points A,B,C,D,E and F lie on the cirumference, so that A,B,C,D,E,F is a regular hexagone(6 equal sides)


    (a): Show that triangle OAB is equilateral, Find its area and the area of the hexagone. Find the area of the circle

    (b) : deduce the area of the minor segment defined on AB

    (c): Find perimeter of this segment
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  2. #2
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    Hello llkkjj24

    Welcome to Math Help Forum!
    Quote Originally Posted by llkkjj24 View Post
    Hi, i really need help on working this one out as it is very important for school, thanks in advance.

    A circle has centre o and radius 1cm, points A,B,C,D,E and F lie on the cirumference, so that A,B,C,D,E,F is a regular hexagone(6 equal sides)


    (a): Show that triangle OAB is equilateral, Find its area and the area of the hexagone. Find the area of the circle

    (b) : deduce the area of the minor segment defined on AB

    (c): Find perimeter of this segment
    (a) All angles at O are equal, because the hexagon is regular. Therefore \angle AOB = 60^o

    AO = OB, radii

    Therefore \angle OAB = \angle ABO (isosceles triangle)

    Therefore \angle OAB = 60^o (angle sum of triangle)

    Therefore \triangle AOB is equilateral.

    Using \triangle = \tfrac12 bc\sin A, its area = \tfrac12.1.1.\sin 60^o = 0.433\, cm^2

    So area of hexagon = 0.433 \times 6 = 2.598\, cm^2.

    Area of circle = \pi.1^2 = 3.142\, cm^2

    (b) Therefore the area of the minor segment AB = \tfrac16(3.142 - 2.598) = 0.088\, cm^2

    (c) Arc AB = \tfrac162\pi.1 = 1.047 \,cm

    AB = 1\, cm

    So the perimeter of this segment = 2.047 \,cm

    Grandad
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  3. #3
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    thank you very much for the help, very detailed
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