Developing Formulas 10 2 Circles and Regular Polygons

Developing Formulas 10 -2 Circles and Regular Polygons Warm Up Lesson Presentation Lesson Quiz Holt. Mc. Dougal Geometry Holt

10 -2 Developing Formulas Circles and 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 Holt Mc. Dougal Geometry

10 -2 Developing Formulas Circles and Regular Polygons Objectives Develop and apply the formulas for the area and circumference of a circle. Develop and apply the formula for the area of a regular polygon. Holt Mc. Dougal Geometry

10 -2 Developing Formulas Circles and Regular Polygons Vocabulary circle center of a regular polygon apothem central angle of a regular polygon Holt Mc. Dougal Geometry

10 -2 Developing Formulas Circles and Regular Polygons Holt Mc. Dougal Geometry

10 -2 Developing Formulas Circles and Regular Polygons Example 1 A: Finding Measurements of Circles Find the area of K in terms of . Holt Mc. Dougal Geometry A = r 2 Area of a circle. A = (3)2 Divide the diameter by 2 to find the radius, 3. A = 9 in 2 Simplify.

10 -2 Developing Formulas Circles and Regular Polygons Helpful Hint The key gives the best possible approximation for on your calculator. Always wait until the last step to round. Holt Mc. Dougal Geometry

10 -2 Developing Formulas Circles and Regular Polygons Example 2: Cooking Application A pizza-making kit contains three circular baking stones with diameters 24 cm, 36 cm, and 48 cm. Find the area of each stone. Round to the nearest tenth. 24 cm diameter A = (12)2 ≈ 452. 4 cm 2 Holt Mc. Dougal Geometry 36 cm diameter A = (18)2 ≈ 1017. 9 cm 2 48 cm diameter A = (24)2 ≈ 1809. 6 cm 2

10 -2 Developing Formulas Circles and Regular Polygons Check It Out! Example 2 A drum kit contains three drums with diameters of 10 in. , 12 in. , and 14 in. Find the circumference of each drum. 10 in. diameter 12 in. diameter 14 in. diameter C = d C = (10) C = (12) C = (14) C = 31. 4 in. C = 37. 7 in. C = 44. 0 in. Holt Mc. Dougal Geometry

10 -2 Developing Formulas Circles and 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 Regular pentagon DEFGH has a center C, apothem BC, and central angle DCE. Holt Mc. Dougal Geometry

10 -2 Developing Formulas Circles and Regular Polygons Holt Mc. Dougal Geometry

10 -2 Developing Formulas Circles and 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 Δ & Label Step 2: Central Angle Step 3: Make Right Δ & Label Step 4: Use Trig Tan(25. 7 o) = 1/a 51. 4 o 25. 7 o 2 Holt Mc. Dougal Geometry Step 5: Plug in A=½a. P 1

10 -2 Developing Formulas Circles and 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. Holt Mc. Dougal Geometry

10 -2 Developing Formulas Circles and Regular Polygons Check It Out! Example 3 Find the area of a regular octagon with a side length of 4 cm. Holt Mc. Dougal Geometry

10 -2 Developing Formulas Circles and Regular Polygons Examples: Find each measurement. 1. the area of D in terms of A = 49 ft 2 2. the circumference of T in which A = 16 mm 2 C = 8 mm Holt Mc. Dougal Geometry

10 -2 Developing Formulas Circles and Regular Polygons Warm Up – 11/18/13 Find each measurement. 3. Speakers come in diameters of 4 in. , 9 in. , and 16 in. Find the area of each speaker to the nearest tenth. A 1 ≈ 12. 6 in 2 ; A 2 ≈ 63. 6 in 2 ; A 3 ≈ 201. 1 in 2 Find the area of each regular polygon to the nearest tenth. 4. a regular nonagon with side length 8 cm A ≈ 395. 6 cm 2 5. a regular octagon with side length 9 ft A ≈ 391. 1 ft 2 Holt Mc. Dougal Geometry

10 -2 Developing Formulas Circles and Regular Polygons Classwork/Homework: • Area of Regular Polygons W/S Holt Mc. Dougal Geometry