Thread: 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

Hello llkkjj24

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Originally Posted by llkkjj24

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

, radii

Therefore (isosceles triangle)

Therefore (angle sum of triangle)

Therefore is equilateral.

Using , its area =

So area of hexagon .

Area of circle

(b) Therefore the area of the minor segment

(c) Arc



So the perimeter of this segment

Grandad

thank you very much for the help, very detailed