How to Find the Area of a Sector of a Circle | Geometry, Circle Sectors, Sector Area
How do we find the sector area of a circle? Sector area can be calculated in a few ways, and we go over two in today's geometry lesson!
To find the area of a sector, remember the beautiful proportionality present in circles! Let's say we are trying to find the area of a sector in a circle with radius r. Suppose the central angle between the two radii that create the sector has a measure of t degrees. Suppose the arc cut by the angle has a length of s. Then, the following equality is all we need,
t/360 = a/pi*r^2 = s/2*pi*r.
Using that equality, which relates the central angle measure, the area of the sector, the radius, and the arc length, we can find the sector area as long as we know the radius length and the central angle or arc length measure.
If t is in radians instead of degrees, the preceding equality is adjusted to
t/2*pi = a/pi*r^2 = s/2*pi*r.
To see exactly how we use this equation to find sector area, watch the video lesson!
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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