1. Areas of Regular Polygons Learning Target: I can use area to model and solve problems.

2. The radius is the distance from the center to a vertex. The apothem is the perpendicular distance from the center to a side.

3. 2 1 3 Finding Angle Measures Ex. Find the measure of each numbered angle. 1. Draw an imaginary circle around the center of the polygon. Knowing that circles are 360 0, divide 360 by the number of sides. 360 0 /5=72 0 m<1=72 0 2. The apothem bisects the vertex angle of the 5 triangles. Therefore m<2=(1/2)m<1 m<2=36 0 3. Knowing the sum of the measures of the angles of a triangle is 180 0, 90+36+m<3=180 0 m <3=54 0

4. 3 2 1 F ind the measure of each numbered angle. m<1=45 0 m <2=22.5 0 m <3=67.5 0

5. Area of a Regular Polygon The area of a regular polygon is half the product of the apothem and the perimeter. a p p A= ap 1 __ 2

6. Finding the Area of a Regular Polygon Find the area of a regular decagon with a 12.3 inch. apothem and 8 in. sides. 12.3 8 A=(1/2)ap Perimeter=10*8=80 A=(1/2)(12.8)(80) A=492

7. Find the area of a regular pentagon with 11.6 cm sides and an 8-cm apothem. (1/2)(8)(11.6*5)= 232

8. Ex. The side of a regular hexagon is 16 ft. Find the area of the hexagon. 16

9. Ex. The side of a regular hexagon is 16 ft. Find the area of the hexagon. 16 360 0 /6=60 0 60 0 8 x Using trig, find the height of the triangle. tan60=8/x x=1.73 A=(1/2)ap A=(1/2)(1.73)(16*6) A=83

10. Ex. An equilateral triangle has a radius of 12.7. Find the area of the triangle. 30 0 12.7 Using trig, find the apothem. sin30=x/12.7 x=6.35 Using trig, find the side length cos30=x/12.7 x=11 this is only half of the side length A=(1/2)ap A=(1/2)(6.35)(22*3) A=210