11 2 Areas of Regular Polygons Warm Up

11. 2 Areas of Regular Polygons Objectives Develop and apply the formula for the

11. 2 Areas of Regular Polygons Vocabulary Apothem Center of a Polygon Radius of

11. 2 Areas of Regular Polygons The center of a regular polygon is equidistant

11. 2 Areas of Regular Polygons Finding the Area of an Equilateral Triangle

11. 2 Areas of Regular Polygons Finding the Area of Regular Polygons Regular pentagon

11. 2 Areas of Regular Polygons To find the area of a regular n-gon

11. 2 Areas of Regular Polygons Example 3 A: Finding the Area of a

11. 2 Areas of Regular Polygons Example 3 A Continued Step 2 Use the

11. 2 Areas of Regular Polygons Example 3 A Continued Step 3 Use the

11. 2 Areas of Regular Polygons Remember! The tangent of an angle in a

11. 2 Areas of Regular Polygons Example 3 B: Finding the Area of a

11. 2 Areas of Regular Polygons Example 3 B Continued Step 2 Use the

11. 2 Areas of Regular Polygons Example 3 B Continued Step 3 Use the

11. 2 Areas of Regular Polygons Check It Out! Example 3 Find the area

11. 2 Areas of Regular Polygons Check It Out! Example 3 Continued Step 2

11. 2 Areas of Regular Polygons Check It Out! Example 3 Continued Step 3

11. 2 Areas of Regular Polygons Lesson Quiz: Find the area of each regular

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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 2. a 45°-90° triangle with leg length 4 in. 3. a 30°-60°-90° triangle with longer leg length 3 m

11. 2 Areas of Regular Polygons Objectives Develop and apply the formula for the area of a regular polygon.

11. 2 Areas of Regular Polygons Vocabulary Apothem Center of a Polygon Radius of a Polygon central angle of a regular polygon

11. 2 Areas of Regular Polygons The center of a regular polygon is equidistant from the vertices. The apothem is the distance from the center to a side. A central angle of a regular polygon has its vertex at the center, and its sides pass through consecutive vertices. Each central angle measure of a regular n-gon is

11. 2 Areas of Regular Polygons Finding the Area of an Equilateral Triangle

11. 2 Areas of Regular Polygons

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.

11. 2 Areas of Regular Polygons To find the area of a regular n-gon with side length s and apothem a, divide it into n congruent isosceles triangles. area of each triangle: total area of the polygon: The perimeter is P = ns.

11. 2 Areas of Regular Polygons

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

11. 2 Areas of Regular Polygons Example 3 A Continued Step 2 Use the tangent ratio to find the apothem. The tangent of an angle is opp. leg. adj. leg Solve for a.

11. 2 Areas of Regular Polygons Example 3 A 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) = 14 ft. A 14. 5 ft 2 Simplify. Round to the nearest tenth.

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.

11. 2 Areas of Regular Polygons Example 3 B: Finding the Area of a Regular Polygon Find the area of a regular dodecagon with side length 5 cm to the nearest tenth. Step 1 Draw the dodecagon. Draw an isosceles triangle with its vertex at the center of the dodecagon. The central angle is . Draw a segment that bisects the central angle and the side of the polygon to form a right triangle.

11. 2 Areas of Regular Polygons Example 3 B Continued Step 2 Use the tangent ratio to find the apothem. The tangent of an angle is Solve for a. opp. leg. adj. leg

11. 2 Areas of Regular Polygons Example 3 B 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. A 279. 9 cm 2 Simplify. Round to the nearest tenth.

11. 2 Areas of Regular Polygons Check It Out! Example 3 Find the area of a regular octagon with a side length of 4 cm. Step 1 Draw the octagon. Draw an isosceles triangle with its vertex at the center of the octagon. The central angle is . Draw a segment that bisects the central angle and the side of the polygon to form a right triangle.

11. 2 Areas of Regular Polygons Check It Out! Example 3 Continued Step 2 Use the tangent ratio to find the apothem The tangent of an angle is opp. leg. adj. leg Solve for a.

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) = 32 cm. A ≈ 77. 3 cm 2 Simplify. Round to the nearest tenth.

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 cm 2 2. a regular octagon with side length 9 ft A ≈ 391. 1 ft 2

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