Geo 10.2 day 25.notebook April 11, 2017 Warm Ups Day 25 1) Find the Area and Circumference 2) Find the area to the nearest tenth. (exact, and to nearest tenth) 5 in. d = 8 in 30o 5 in. 3) Find the lower base if Area = 70 in . 2 7 in. x Apr 910:52 AM Get Ch 7 test back. Apr 1110:43 AM 1 Geo 10.2 day 25.notebook April 11, 2017 Questions on HW 24 pg 681? Apr 91:21 PM Mar 296:02 PM 2 Geo 10.2 day 25.notebook April 11, 2017 Apr 91:22 PM pass in Mar 296:02 PM 3 Geo 10.2 day 25.notebook April 11, 2017 10.2 GOALS 1) Develop and apply the formulas for the area and circumference of a circle. 2) Develop and apply the formula for the area of a regular polygon. Apr 910:50 AM Why is the area of a circle It all started with the discovery that ?? <circumference <diameter d Mar 296:11 PM 4 Geo 10.2 day 25.notebook April 11, 2017 > Sep 135:38 PM > Sep 135:42 PM 5 Geo 10.2 day 25.notebook April 11, 2017 > Sep 135:44 PM Parallelogram! > | 1_ C | 2 A = 1_2 d r 1 _ A = 2 2r r r2 A = Sep 135:44 PM 6 Geo 10.2 day 25.notebook April 11, 2017 A circle is named by the symbol ¤ and its center. ¤A or radius AB, AD, AC diameter CD Apr 911:01 AM CW 25 in groups 1) Find the area of ¤K in terms of π. 1 2) Find the radius of ¤J if the circumference is (100π )m. 3) Find the circumference of ¤M if the area is (25π)ft2 4) Find the area of ¤A in terms of π in which C = (4π) m. Apr 911:06 AM 7 Geo 10.2 day 25.notebook April 11, 2017 Break Apr 111:06 PM Vocab Notes Center of a regular polygon A point equidistant from the vertices. B Radius A segment that connects the center to a vertex Apothem A A segment that connects center to a side _| C D Central Angle An angle whose vertex is at the center and its sides pass through consecutive vertices. Each central angle measure of a regular ngon is Apr 127:41 AM 8 Geo 10.2 day 25.notebook April 11, 2017 What is the value of one central angle of each regular polygon? 3 sides 6 sides 4 sides 7sides 5 sides 8 sides Apr 911:37 AM Regular pentagon DEFGH Name each: vertex 1) ∠FGH ____ central angle 2) ∠GCH ____ center 3) point C ____ apothem 4) segment BC ____ radius 5) segment CF ____ Apr 911:30 AM 9 Geo 10.2 day 25.notebook April 11, 2017 Can we find the area of a regular polygon given a side length? 6 cm Mar 296:36 PM Can we find the area of a regular polygon given a side length? 6 Mar 296:36 PM 10 Geo 10.2 day 25.notebook April 11, 2017 Can we find the area of a regular polygon given a side length? 6 Mar 296:36 PM Can we find the area of a regular polygon given a side length? 6 Mar 296:36 PM 11 Geo 10.2 day 25.notebook April 11, 2017 Can we find the area of a regular polygon given a side length? 6 173.8 cm 2 Mar 296:36 PM Find the area of regular heptagon with side length 2 ft to the nearest tenth. 2 ft Apr 911:31 AM 12 Geo 10.2 day 25.notebook April 11, 2017 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. The central angle is _____. 2 ft. 51.4o Step 2 Draw the triangle formed by the central angle. Draw the apothem, which bisects the central angle and the side of the polygon to form a right triangle. 51.4o 2 ft. Apr 912:16 PM Step 3 Use the tangent ratio to find the apothem. 51.4o 2 ft. 51.4o 2 ft Apr 912:25 PM 13 Geo 10.2 day 25.notebook April 11, 2017 Step 4 Use the apothem and the given side length to find the area. Apr 912:34 PM Find the area of a regular dodecagon with side length 5 cm to the nearest tenth. Step 1 Draw the dodecagon. The central angle is_____. Step 2 Draw the triangle formed by the central angle. Draw the apothem, which bisects the central angle and the side of the polygon to form a right triangle. Step 3 Use the tangent ratio to find the apothem. Step 4 Use the apothem and the given side length to find the area. Apr 912:36 PM 14 Geo 10.2 day 25.notebook April 11, 2017 Find the area of a regular dodecagon with side length 5 cm to the nearest tenth. 5 cm Apr 912:38 PM Find the area of the regular hexagon that has a distance of 15 inches from the center to the vertices. 15 in. Apr 912:49 PM 15 Geo 10.2 day 25.notebook April 11, 2017 A regular triangle with an apothem of 10 inches. Find the area of the triangle. 10 Apr 91:39 PM HW 25 pg 691 #4, 69, 1826, 28, 30 Apr 94:16 PM 16
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