11.6 –Areas of Regular Polygons
Center of a polygon: Point equidistant to the vertices of the of the polygon P
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 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 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 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 17.1°
2. Find the given angle measure for the regular hexagon shown. Each central angle = 60° m EGF = 60° 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. 4 2 = a = a = a 2 Apothem = _____________ A = ____________________
5. Find the area of the polygon. c 2 = a 2 + b = a = a = a 5.5 Apothem = _____________ A = ____________________ 5.5in = a
m ACB = _______ 12cm 120° 60° 24cm Apothem = ___________ A = __________________ 6. Find the area of the polygon. 30°
6. Find the area of the polygon. 30°60°90° 1 2 12cm m ACB = _______ 120° Apothem = ___________ A = __________________ 30°
6. Find the area of the polygon. 12cm m ACB = _______ 120° Apothem = ___________ A = __________________
60° 30° 5m 7. Find the area of the polygon. 5m m ACB = _______ 60° Apothem = ___________ A = __________________ 60°
7. Find the area of the polygon. 30°60°90° ° 5m m ACB = _______ 60° Apothem = ___________ A = __________________ 60°
7. Find the area of the polygon. 30° 5m m ACB = _______ 60° Apothem = ___________ A = __________________
72° 36° 8. Find the area of the polygon. m ACB = _______ 72° Side Length = ________ A = __________________
36° SOH – CAH – TOA 1 = x15.98 O A H 8. Find the area of the polygon. m ACB = _______ 72° Side Length = ________ A = __________________ 31.96cm
36° O A H 8.Find the area of the polygon. m ACB = _______ 72° Side Length = ________ A = __________________ 31.96cm
45° 22.5° 9. Find the area of the polygon. m ACB = __________ Apothem = __________ Side Length = ________ A = __________________
22.5° SOH – CAH – TOA 1 = a5.54 O A H 1 = x Find the area of the polygon. m ACB = __________ Apothem = __________ Side Length = ________ A = __________________ 45° 5.54in 4.6in 2.3
22.5° 5.54 O A H Find the area of the polygon. m ACB = __________ Apothem = __________ Side Length = ________ A = __________________ 45° 5.54in 4.6in