# Thread: finding areas perimeters and segments in circle

1. ## 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

2. Hello llkkjj24

Welcome to Math Help Forum!
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 $\displaystyle \angle AOB = 60^o$

$\displaystyle AO = OB$, radii

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

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

Therefore $\displaystyle \triangle AOB$ is equilateral.

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

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

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

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

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

$\displaystyle AB = 1\, cm$

So the perimeter of this segment $\displaystyle = 2.047 \,cm$

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

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