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° 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°

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° 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° 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. Apothem = _____________ A = ____________________

5. Find the area of the polygon. c2 = a2 + b2 6.82 = a2 + 42 46.24 = a2 + 16 30.24 = a2 5.5 5.5 = a 5.5in Apothem = _____________ A = ____________________

24cm 6. Find the area of the polygon. 120° 60° 60° 12cm 12cm 30° 12cm 12cm 24cm mACB = _______ 120° Apothem = ___________ A = __________________

1 2  6. Find the area of the polygon. 30° 60° 90° mACB = _______ 12cm 12cm  mACB = _______ 120° Apothem = ___________ A = __________________

6. Find the area of the polygon. 12cm 12cm mACB = _______ 120° Apothem = ___________ A = __________________

7. Find the area of the polygon. 60° 30° 60° 5m 5m mACB = _______ 60° Apothem = ___________ A = __________________

1 2 7. Find the area of the polygon. 5m 30° 60° 90° mACB = _______ Apothem = ___________ A = __________________

7. Find the area of the polygon. 30° 5m mACB = _______ 60° Apothem = ___________ A = __________________

8. Find the area of the polygon. 72° 36° mACB = _______ 72° Side Length = ________ A = __________________

H A O 8. Find the area of the polygon. SOH – CAH – TOA 1 15.98 = x 36° H A 15.98 = x 15.98 15.98 O mACB = _______ 72° 31.96cm Side Length = ________ A = __________________

H A O 15.98 15.98 mACB = _______ 72° 31.96cm Side Length = ________ Find the area of the polygon. 36° H A 15.98 15.98 O mACB = _______ 72° 31.96cm Side Length = ________ A = __________________

A = __________________ 45° 9. Find the area of the polygon. 45° 22.5° mACB = __________ Apothem = __________ Side Length = ________ A = __________________ 45°

H A O SOH – CAH – TOA 1 5.54 = a 2.3 2.3 1 mACB = __________ 9. Find the area of the polygon. SOH – CAH – TOA 1 H A 22.5° 5.54 5.54 = a 2.3 2.3 O 1 mACB = __________ Apothem = __________ Side Length = ________ A = __________________ 45° 5.54in 4.6in 2.3 = x

H A O 2.3 2.3 mACB = __________ Apothem = __________ 9. Find the area of the polygon. H A 22.5° 5.54 2.3 O 2.3 mACB = __________ Apothem = __________ Side Length = ________ A = __________________ 45° 5.54in 4.6in

HW Problems 11.6 765-767 1-4, 8-11, 14-16, 19-21 #20 H 36° O 2.98 A 2.98 SOH – CAH – TOA 29.8u 2.98 = x