Difference between revisions of "Sector"

Revision as of 19:37, 24 April 2008

$[asy]size(150); real angle1=30, angle2=100; pair O=origin, A=dir(angle2), B=dir(angle1); path sector=O--B--arc(O,1,angle1,angle2)--A--cycle; fill(sector,gray(0.9)); D(unitcircle); D(A--O--B); MP("O",D(O),SSW); MP("A",D(A),NNW); MP("B",D(B),NE); MP("\theta",(0.075,0.075),N);[/asy]$

A sector of a circle $O$ is a region bounded by two radii of the circle, $OA$ and $OB$ , and the arc $AB$ .

Area

The area of a sector $AOB$ , where $\theta=\angle AOB$ is in radians, is found by multiplying the area of circle $O$ by $\frac{\theta}{2\pi}$ .

Therefore, the area of a sector $AOB$ , where $r$ is the radius and $\theta=\angle AOB$ is in radians, is $\frac{\theta r^2}{2}$ .

Alternatively, if $\theta$ is in degrees, the area is $\frac{\theta \pi r^2}{360^{\circ}}$ .

This article is a stub. Help us out by expanding it.

@@ Line 8: / Line 8: @@
 MP("O",D(O),SSW);
 MP("A",D(A),NNW);
-MP("B",D(B),NE);</asy></div>
+MP("B",D(B),NE);
+MP("\theta",(0.075,0.075),N);</asy></div>
 A '''sector''' of a [[circle]] <math>O</math> is a region bounded by two [[radius|radii]] of the circle, <math>OA</math> and <math>OB</math>, and the [[arc]] <math>AB</math>.
+== Area ==
+The [[area]] of a sector <math>AOB</math>, where <math>\theta=\angle AOB</math> is in radians, is found by [[multiply]]ing the area of circle <math>O</math> by <math>\frac{\theta}{2\pi}</math>.
+Therefore, the area of a sector <math>AOB</math>, where <math>r</math> is the radius and <math>\theta=\angle AOB</math> is in radians, is <math>\frac{\theta r^2}{2}</math>.
+Alternatively, if <math>\theta</math> is in degrees, the area is <math>\frac{\theta \pi r^2}{360^{\circ}}</math>.
 {{stub}}
 [[Category:Definition]]
 [[Category:Geometry]]

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Difference between revisions of "Sector"

Revision as of 19:37, 24 April 2008

Area