11.2 Vocabulary Population Density Sector of a Circle Segment of a Circle

You can use the circumference of a circle to find its area You can use the circumference of a circle to find its area. Divide the circle and rearrange the pieces to make a shape that resembles a parallelogram. The base of the parallelogram is about half the circumference, or r, and the height is close to the radius r. So A   r · r =  r2. The more pieces you divide the circle into, the more accurate the estimate will be.

Similar to arc length, the area of a sector is a fractional part of the circle area.

A segment of a circle is a region bounded by an arc and its chord.

In a 30°-60°-90° triangle, the length of the leg opposite the 60° angle is √3 times the length of the shorter leg. x, x√3, 2x In a 45°-45°-90° triangle, the length of the leg opposite the 90° angle is √2 times the length of the shorter legs. x, x, x√2 Remember!

Example 5A: Finding the Area of a Segment Find the area of segment LNM to the nearest hundredth.

Example 5B Find the area of segment RST to the nearest hundredth.