Name “N-GON” Circle
# of sides 3 4 5 6 8 n NA
Measure Central Angle NA
Measure internal angle NA
Side length in terms of radius
NA
Perimeter (in terms of radius)
Apothem (a) (in terms of radius) .80802r .9239r
Area (in terms of radius)
Name Equilateral Triangle
Square Pentagon Hexagon Octagon “N-GON” Circle
# of sides 3 4 5 6 8 n NA
Measure Central Angle NA
Measure internal angle NA
Side length in terms of radius
NA
Perimeter (in terms of radius) 2r*Π
Apothem (a) (in terms of radius) .80802r .9239r r
Area (in terms of radius) Πr^2
NameEquilateral Triangle
Square Pentagon Hexagon Octagon “N-GON” Circle
# of sides 3 4 5 6 8 n NA
Measure Central Angle 120 90 NA
Measure internal angle 60 90 NA
Side length in terms of radius r√3
= 1.73rr√2
=1.41rNA
Perimeter (in terms of radius) 4r√3
=5.20r4 r√2
=5.66r2r*Π
Apothem (a) (in terms of radius)
r/2=.5r
r√2/2.71r
.80802r .9239r R
Area (in terms of radius) r2 (3/4)√3
=1.30 r2 2 r2 Πr2
=3.14r2
Triangles
Find: Central Angle
Whole circle is 3600
There are 3 angles that make up 3600 thus Measure of central angle is = 360/3
Central Angle of triangle =1200
Triangles To find: Interior AngleMeasure of central=120Sum of all angles in the blue triangle is 180
each side angle will be = (180-120)/2 = 300
Interior Angle
Interior Angle= 2* 300
= 600
Triangles
Total Area = 3*Area of ORANGE TRIANGLE
Area ORANGE TRIANGLE= ½ b*a = ½ r√3 *r/2 = (r2/4)√3
= r2 (3/4)√3
r√3
r/2
SquareFind: Central Angle
Whole circle is 3600
There are 4 angles that make up 3600 thus Measure of central angle is = 360/4 = 900
Square
r
r
r/√2
r/√2= r√2/2
45
45
Apothem = r√2/2
Side Length = 2 * r√2/2 = r√2
Perimeter = 4*side length = 4r√2
Square
45
45
r√2
r√2/2
Total Area = 4*Area of BLUE TRIANGLE
Area BLUE TRIANGLE= ½ b*a = ½ r√2 *r√2/2 = (r2/2)
= 2r2
NameEquilateral Triangle
Square Pentagon Hexagon Octagon “N-GON” Circle
# of sides 3 4 5 6 8 n NA
Measure Central Angle
120 90 72 60 45 NA
Measure internal angle
60 90 108 120 135 NA
Side length in terms of radius
r√3 = 1.73r
r√2=1.41r
1.1756r r .76537r NA
Perimeter (in terms of radius)
4r√3=5.20r
4 r√2=5.66r
5.8778r 6r 6.123r 2r*Π
Apothem (a) (of radius)
r/2=.5r
r√2/2.71r
.80802rr√3/2
= .866r.9239r R
Area (in terms of radius)
r2 (3/4)√3=1.30 r2 2 r2 2.378 r2
3√3/2r2
=2.598r22.828 r2 Πr2
=3.14r2
Name Equilateral Triangle
Square Pentagon Hexagon Octagon “N-GON” Circle
# of sides 3 4 5 6 8 N NA
Measure Central Angle
120 90 72 60 45 360/n NA
Measure internal angle
60 90 108 120 135180(n-2)
nNA
Side length in terms of radius
r√3 = 1.73r
r√2=1.41r
1.1756r r .76537r 2√(r2 - a2) NA
Perimeter (in terms of radius)
4r√3=5.20r
4 r√2=5.66r
5.8778r 6r 6.123rn*side=
2n√(r2 - a2) 2r*Π
Apothem (a) (of radius)
r/2=.5r
r√2/2.71r
.80802rr√3/2
.865.9239r
Find out after trig!
R
Area (in terms of radius)
r2 (3/4)√3=1.30 r2 2 r2 2.378 r2
(3√3/2)r2
=2.598r22.828 r2 ½ a*p
Πr2
=3.14r2
Ex 3.) Find the shaded & un-shaded region of the equilateral triangle with side length 2 inscribed in the circle.
Ex 4.) Given 3 shapes: A square with diagonal length = 6, A regular hexagon with diagonal length= 6, and a circle with diameter equal to 6. Which of the following is true.
A. Area Square < Area hexagon < Area Circle
B. Area Square > Area hexagon > Area Circle
C. Area Square = Area hexagon = Area Circle
D. Area Square > Area Circle > Area hexagon
E. It is impossible to tell from the information given