Pearson Geometry Common Core, 2011
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Pearson Geometry Common Core, 2011 View details
7. Areas of Circles and Sectors
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Exercise 27 Page 664

A part of a circle bounded by an arc and the segment joining its endpoints is a segment of a circle.

To find the area of a segment for a minor arc, we need to draw radii to form a sector. The area of the segment equals the area of the sector minus the area of the triangle formed.

For the given diagram, we will find the area of the sector and then the area of the triangle. Next, we will find their difference to find the area of the segment. Finally, we will calculate the difference between the area of the circle and the area of the segment to find the area of the shaded region.

Area of the Sector

The area of a sector of a circle is the product of the measure of the arc divided by and the area of the circle.