area and perimeter: areas of regular polygons
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Area and Perimeter: Areas of Regular Polygons. inscribed polygon circumscribed circle. Review: Inscribed Polygons & Circumscribed Circles. Inscribed means written inside. Circumscribed means written around (the outside). - PowerPoint PPT PresentationTRANSCRIPT
Review: Inscribed Polygons & Circumscribed Circles
Inscribed means written inside
Circumscribed means written around (the outside)
Def: A polygon is inscribed in a circle & the circle is circumscribed about the polygon when each vertex of the polygon lies on the circle.
inscribed polygoncircumscribed circle
Def: A ________________is a polygon that is equiangular & equilateral.
Inscribed Regular Polygons & Triangles
Total of Interior Angles = ___________Each Interior Angle = ______________
Inscribed Regular Pentagon
5 congruent isosceles triangles
Total of Central Angles = _________Each central angle = _____________
Parts of a Regular Polygon A stands for Area
A(nonagon) is the area of a regular 9-sided figure.
n is the number of sides of a regular polygon p is perimeter, r is radius, s is side a is apothem
____________ – The line segment from the center of a regular polygon to the midpoint of a side or the length of this segment.
Sometimes known as the ______________, or the radius of a regular polygon’s inscribed circle.
Regular Polygon Area Theorem
Regular Polygon Area Theorem: The area of a regular polygon is _______________________________________________________________________________________________
A(n-gon) =
=n1
2sa
=1
2a(ns)
YX s
O
a
Given: an inscribed regular n-gon (shown as an octagon)
Regular Polygon Terminology
_______________________- the center of the circumscribed circle (O).
_______________________- the distance from the center to a vertex (OX).
____________________________- the (perpendicular) distance from the center of the polygon to a side. (OM)
_____________________________- an angle formed by 2 radii drawn to consecutive vertices. ( )∠XOY
YX M
O (Regular Octagon)
Example: Square
A=12aphyp=leg 2
8 2 =a 2
p=ns
p=4(2x)
p=4[(2)(8)]
=1
28(64)45
x =a=8r a
r = . Find a, p, A.8 2
s
x
Example: Equilateral Triangle
A=12aphyp=2short p=ns
x = 3(4)
p=3(2x)
long= 3 short30
ra
s
a = 4. Find r, p, A .
x
Example: Regular Hexagon
A=12aplong= 3 short
a= 3 x
p=ns
=6(2)(5)
hyp=2 short
r =2(5)
=6(2x)
=6060
r =10
s
a = . Find r, p, A.5 3
r a
x
Regular Nonagon
A=12ap
a=9.397
sin X =opphyp
sin 70 =a10
p=ns
cosX =adjhyp
=1
2(9.397)(61.56)
=9(2x)
cos 70 =x10
70
a=10(.9397 ) =289.24
r = 10; Find a, p, A.
r a
x
s
X
x=10(.3420 )
x=3.420
p=9(2)(3.420 )
p=61.56