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If the sector has a radius, , and a radian angle measure of , we have already seen that we could nd its arc length by multiplying times . What is the area of this sector? We could nd that by measuring the area of the region inside the full circle, and multiplying by what fraction of the circle we have. Since the full circle would have a radian measure of ,
we must have of the full circle. Therefore the area is . For example,
if our pizza slice had a radius inches and a radian angle measure of , the area of the entire pizza pie would be square inches and our slice would be of the entire pizza, so its area would be square inches which is a little more than square inches.
Unit 7
Lesson 4: Area of a Sector
45
