Find the Area

10-5: Area of Regular Polygonsp. 543-550

Primary:

M(G&M)–10–6 Solves problems involving perimeter, circumference, or area of two-dimensional figures (including composite figures) or surface area or volume of three-dimensional figures (including composite figures) within mathematics or across disciplines or contexts.

Secondary:

GSE’s

M(G&M)–10–9 Solves problems on and off the coordinate plane involving distance, midpoint, perpendicular and parallel lines, or slope.

Area of any Regular Polygon = Pa2

1

perimeter of the polygon

a = apothem (the segment from the center of the polygon to the side (where it is perpendicular)

a

**All regular polygons can be inscribed within a circle

a = apothem

Find the area of the regular polygon described.

A triangle with a side length of 14 inches

A regular hexagon with a perimeter of 36 meters

ExEx: Find the area of the shaded region.: Find the area of the shaded region.

4 cm4 cm

regionshadedo AAA

r2

4

32s

4 cm4 cm

3030oo22

22ðð33

44ðð33

(4)2

16

4

3342

4

3316

4

348 312

1616 - 12 - 12ðð3 3

= 29.5 cm= 29.5 cm22

http://guilford.rps205.com/departments/Math/Links/Honors%20Geometry/Honors%20Geometry%20Power%20Points/11.2%20%20Area%20of%20reg%20polygons.ppt#7

Ex: A regular octagon has a radius Ex: A regular octagon has a radius of 4 in. Find its area.of 4 in. Find its area.

First, we have to find the First, we have to find the apothem length.apothem length.

4sin67.5 = a4sin67.5 = a

3.7 = a3.7 = a

Now, the side length.Now, the side length.

Side length=2(1.53)=3.06Side length=2(1.53)=3.06

44

aa

135135oo

67.567.5oo

45.67sin

a

3.73.7

xx

45.67cos

x

4cos67.5 = x4cos67.5 = x

1.53 = x1.53 = x

A = ½ PaA = ½ Pa = ½ (24.48)(3.7)= ½ (24.48)(3.7) = 45.288 in= 45.288 in22

http://guilford.rps205.com/departments/Math/Links/Honors%20Geometry/Honors%20Geometry%20Power%20Points/11.2%20%20Area%20of%20reg%20polygons.ppt#7

Homework