11.6 –Areas of Regular Polygons. Center of a polygon: Point equidistant to the vertices of the polygon center.

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Presentation transcript:

11.6 –Areas of Regular Polygons

Center of a polygon: Point equidistant to the vertices of the polygon center

Radius of a polygon: Length from the center to the vertex of a polygon

Apothem of the polygon: Length from the center to the side of a polygon

Central angle of a regular polygon: Angle formed by two radii in a polygon

1. Find the measure of a central angle of a regular polygon with the given number of sides. Round answers to the nearest tenth of a degree if necessary. 6 sides Central Angle = 60°

1. Find the measure of a central angle of a regular polygon with the given number of sides. Round answers to the nearest tenth of a degree if necessary. 12 sides Central Angle = 30°

1. Find the measure of a central angle of a regular polygon with the given number of sides. Round answers to the nearest tenth of a degree if necessary. 40 sides Central Angle = 9°9°

1. Find the measure of a central angle of a regular polygon with the given number of sides. Round answers to the nearest tenth of a degree if necessary. 21 sides Central Angle = 17.1°

2. Find the given angle measure for the regular hexagon shown. Each central angle = 60°

2. Find the given angle measure for the regular hexagon shown. m  EGF = 60°

2. Find the given angle measure for the regular hexagon shown. m  EGD = 60°

2. Find the given angle measure for the regular hexagon shown. m  EGH = 30° 60° 30°

2. Find the given angle measure for the regular hexagon shown. m  DGH = 30° 60° 30°

2. Find the given angle measure for the regular hexagon shown. m  GHD = 90°

Area of a regular polygon: s = side length a = apothem length n = number of sides

3. A regular pentagon has a side length of 8in and an apothem length of 5.5in. Find the area.

4. Find the area of the polygon. Central Angle = _______ Central Angle = 60°

4. Find the area of the polygon. c 2 = a 2 + b = a = a = a 2 Apothem = __________

5. Find the area of the polygon. Central Angle = _______ Central Angle = 72°

5. Find the area of the polygon. c 2 = a 2 + b = a = a = a = a 5.5 Apothem = __________

6. Find the area of the polygon. m  ACB = _______ 12cm Central Angle = 120° 60° 24cm 30°

6. Find the area of the polygon. 30°60°90° 1  2 12cm Apothem = __________ 30°

6. Find the area of the polygon. 12cm 30°

m  ACB = _______ Central Angle = 60° 30° 5m 7. Find the area of the polygon. 5m 60°

7. Find the area of the polygon. 30°60°90° ° 5m Apothem = __________ 60°

7. Find the area of the polygon. 30° 5m

8. Find the area of the polygon. m  ACB = _______ Central Angle = 72° 36°

8. Find the area of the polygon. 36° SOH – CAH – TOA 1 = x15.98 Side Length = __________ cm

8. Find the area of the polygon. Round to two decimal places. 36° 15.98

m  ACB = _______ Central Angle = 45° 22.5° 9. Find the area of the polygon. Round to two decimal places.

22.5° SOH – CAH – TOA 1 = a Find the area of the polygon. Round to two decimal places. apothem = _______ 5.54 in

22.5° SOH – CAH – TOA 1 = x Find the area of the polygon. Round to two decimal places. Side length = _______ 4.6 in

22.5° Find the area of the polygon. Round to two decimal places.