Area of a Segment

Question

Hello there, long time since I've done Maths at any level, and I'm having some problems getting my head around this question.

 

[IMG]http://img832.imageshack.us/img832/1778/tuai.jpg[/IMG]

 

I've dug out some old books... and found out that...

 

(x = angle in degrees)

 

Area of circle = Pi x r squared

 

Area of sector = (x/360) x Area of full circle

 

Area of segment = Area of sector - area of triangle

 

So I think I found out the area of the sector ok as it came to Pi.

 

Area of circle = Pi * 2 squared = 4Pi

 

Then... area of sector = (90/360) * 4 Pi

 

Which equals Pi.

 

But now I'm completely thrown by the area of the segment...

 

Can anyone advise on the next step(s)?

 

Thank you.

 

Answer 1

serkel sekter=2 raes out from senter tu rim av serkel...pie shape

sekter area=[(angel tween 2 lines out) /(2*pi)]* area av serkel...=pi*r*r

Draw a strate line tween the 2 points on serkel rim weer the 2 raes from senter hit rim.

this is the "chord" in tipikal guvt krat speek.  It kut sekter intu 2 peeses...

segment=part tween chord & serkel rim.

triangel=part from serkel senter tu the chord.

segment area=sekter area - triangel area.

triangel area=radius*(chord-leng/2)

(chord-leng/2)=radius*sine(angel/2)