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11-2. Areas of Regular Polygons. Warm Up. Lesson Presentation. Lesson Quiz. Holt Geometry. 11.2 Areas of Regular Polygons. Warm Up Find the unknown side lengths in each special right triangle. 1. a 30°-60°-90° triangle with hypotenuse 2 ft.

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11-2

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  1. 11-2 Areas of Regular Polygons Warm Up Lesson Presentation Lesson Quiz Holt Geometry

  2. 11.2 Areas of Regular Polygons Warm Up Find the unknown side lengths in each special right triangle. 1. a 30°-60°-90° triangle with hypotenuse 2 ft 2. a 45°-45°-90° triangle with leg length 4 in. 3. a 30°-60°-90° triangle with longer leg length 3m

  3. 11.2 Areas of Regular Polygons Objectives Develop and apply the formula for the area of a regular polygon.

  4. 11.2 Areas of Regular Polygons Vocabulary Apothem Center of a Polygon Radius of a Polygon central angle of a regular polygon

  5. 11.2 Areas of Regular Polygons The center of a regular polygonis equidistant from the vertices. The apothemis the distance from the center to a side. A central angle of a regular polygonhas its vertex at the center, and its sides pass through consecutive vertices. Each central angle measure of a regular n-gon is

  6. 11.2 Areas of Regular Polygons Finding the Area of an Equilateral Triangle

  7. 11.2 Areas of Regular Polygons

  8. 11.2 Areas of Regular Polygons Finding the Area of Regular Polygons Regular pentagon DEFGH has a center C, apothem BC, and central angle DCE.

  9. 11.2 Areas of Regular Polygons area of each triangle: total area of the polygon: To find the area of a regular n-gon with side length s and apothem a, divide it into n congruent isosceles triangles. The perimeter is P = ns.

  10. 11.2 Areas of Regular Polygons

  11. 11.2 Areas of Regular Polygons Step 1 Draw the heptagon. Draw an isosceles triangle with its vertex at the center of the heptagon. The central angle is . Example 3A: Finding the Area of a Regular Polygon Find the area of regular heptagon with side length 2 ft to the nearest tenth. Draw a segment that bisects the central angle and the side of the polygon to form a right triangle.

  12. 11.2 Areas of Regular Polygons The tangent of an angle is . opp. leg adj. leg Example 3A Continued Step 2 Use the tangent ratio to find the apothem. Solve for a.

  13. 11.2 Areas of Regular Polygons Example 3A Continued Step 3 Use the apothem and the given side length to find the area. Area of a regular polygon The perimeter is 2(7) = 14ft. Simplify. Round to the nearest tenth. A 14.5 ft2

  14. 11.2 Areas of Regular Polygons Remember! The tangent of an angle in a right triangle is the ratio of the opposite leg length to the adjacent leg length. See page 525.

  15. 11.2 Areas of Regular Polygons Step 1 Draw the dodecagon. Draw an isosceles triangle with its vertex at the center of the dodecagon. The central angle is . Example 3B: Finding the Area of a Regular Polygon Find the area of a regular dodecagon with side length 5 cm to the nearest tenth. Draw a segment that bisects the central angle and the side of the polygon to form a right triangle.

  16. 11.2 Areas of Regular Polygons The tangent of an angle is . opp. leg adj. leg Example 3B Continued Step 2 Use the tangent ratio to find the apothem. Solve for a.

  17. 11.2 Areas of Regular Polygons Example 3B Continued Step 3 Use the apothem and the given side length to find the area. Area of a regular polygon The perimeter is 5(12) = 60 ft. Simplify. Round to the nearest tenth. A 279.9 cm2

  18. 11.2 Areas of Regular Polygons Step 1 Draw the octagon. Draw an isosceles triangle with its vertex at the center of the octagon. The central angle is . Check It Out! Example 3 Find the area of a regular octagon with a side length of 4 cm. Draw a segment that bisects the central angle and the side of the polygon to form a right triangle.

  19. 11.2 Areas of Regular Polygons The tangent of an angle is . opp. leg adj. leg Check It Out! Example 3 Continued Step 2 Use the tangent ratio to find the apothem Solve for a.

  20. 11.2 Areas of Regular Polygons Check It Out! Example 3 Continued Step 3 Use the apothem and the given side length to find the area. Area of a regular polygon The perimeter is 4(8) = 32cm. Simplify. Round to the nearest tenth. A ≈ 77.3 cm2

  21. 11.2 Areas of Regular Polygons Lesson Quiz: Find the area of each regular polygon to the nearest tenth. 1. a regular nonagon with side length 8 cm A ≈ 395.6 cm2 2. a regular octagon with side length 9 ft A ≈ 391.1 ft2

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