11.1.3 Sector Area and Arc Length Key Objectives • Find the area of sectors. • Find arc lengths. Key Terms • A sector of a circle is a region bounded by two radii of the circle and their intercepted arc.
• A segment of a circle is a region bounded by an arc and its chord. • Arc length is the distance along an arc measured in linear units. Formulas • Sector Area = A πr 2
⎛ ⎝ ⎜⎜ ⎛ ⎝ ⎜⎜
⎞ ⎠ ⎟⎟ ⎞ ⎠ ⎟⎟
m 360
m
• Arc Length
= L πr 2
360
Example 1 Finding the Area of a Sector
The area of a sector is determined in this example. The radius and the measure of the central angle are given. To determine the area of the sector DAE , use the formula for the area of a sector. Substitute the given values for radius and the measure of the central angle into the formula. Solving for area yields A ≈ 32.7 in 2 .
Example 2 Agriculture Application
The area of a sector is determined in this application example. The diameter and the measure of the central angle are given. To determine the area of the sector covered by the irrigation system, use the formula for the area of a sector. Divide the diameter by 2 to find the radius. Substitute the values for radius and the measure of the central angle into the formula. Solving for area yields A ≈ 20,944 ft 2 .
243
Made with FlippingBook - PDF hosting