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Arc Lengths and Areas of Sectors Lesson 11.6 Geometry Honors

Arc Lengths and Areas of Sectors Lesson 11.6 Geometry Honors. Objective: Know and use the formulas for Arc Lengths and Areas of Sectors. Lesson Focus. This lesson shows how the length of an arc of a circle and the area of a region or sector of a circle can be calculated. Basic Terms.

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Arc Lengths and Areas of Sectors Lesson 11.6 Geometry Honors

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  1. Arc Lengths and Areas of SectorsLesson 11.6Geometry Honors Objective: Know and use the formulas for Arc Lengths and Areas of Sectors.

  2. Lesson Focus This lesson shows how the length of an arc of a circle and the area of a region or sector of a circle can be calculated.

  3. Basic Terms Sector of a Circle A region bounded by two radii and an arc of the circle.

  4. Arc Length

  5. Arc Length If the measure of minor arc AB = x°, then the length of minor arc AB = (x°/360°)(2πr) Do not confuse arc measure with arc length. Arc measure equals the measure of the corresponding central angel and is independent of the size of the circle. Arc length depends on the size of the circle because it is a part of the circumference of the circle.

  6. Area of a Sector

  7. Area of a Sector If the measure of minor arc AB = x°, then the area of sector AOB = (x°/360)(πr2) Except for special cases, finding the area of a region bounded by a chord and its arc usually requires the use of trigonometry.

  8. Practice The radius of a circle is 3 cm. Find (a) the lengths of the given arcs, and (b) the areas of the sectors determined by the given arcs. • 50° • 20° • 140°

  9. Written Exercises Problem Set 11.6, p.453: # 2 – 14 (even) Handout: 11-6

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