Download - 11.6 Areas of Regular Polygons Notes
3 0 0 Le s s o n 1 1 . 6 ·
G e o m e t ry
N M e t a k l n g O u ld e C o p y rig h t 0 M c D o u g a l L H te [l/ H o u g h to n M lfM n C o m p a n y .
m Z H E G =.
S o , + + m Z H E G = 1 8 0
°
! a n d
c . T h e s u m o f t h e m e a s u re s o f rig h t A H E G is 1 8 0 °
m Z E G H = m Z E G F =.
o f ıs o s c e le s A E G F . S o , G H Z E G F a n d
b . G H ıs a n a p o t h e m , w h ıc h m a k e s It a n
a . Z E G F ıs a c e n t ra ı a n g e , s o m Z E G F =, o r
s o ıu t ıo n
c . m Z H E G
月 广
b . M Z E G H
a . M Z E G F
W LB V G J .a n g e m e a s u re .
h e x a g o n ın s c rıb e d In O G . F ın d e a c h
"
\
In t h e d ıa g ra m , A B C D E F ls a r e g u ıa r
E x a m p \ e 1 F in d a n gle m e a s u re s in a re g u ıa r p o ly g o n
C e n t ra ı a n g e o f a re g u la r p o ly g o n
A p o t h e m o f a p o ly g o n
R R
C e n te r o f a p o ıy g o n
V O C A B U L A R Yy o u r N o te s
/ « io a ıi · F in d a re a s o f re g u la r p o ly g o n s in s c rib e d in c irc le s .
I 1 1 1 0 1 A re a s o f R e g u ıa r P o ıy g o n sI a % ·
C o p w ig h t e M c D o u g a l U tte ll/ H o u g h to n M ifn in C o m p a ru . L e s s o n 1 1 . 6 ·
G ı o m ı tr r
N o t e t a k ı n g G u ld a 3 0 1
c e n t im e t e rs .
T h e a re a o f t h e c o a s t e r is a b o u t s q u a re
Sım p lıń r.i
/ ı
し
ウアー
ー )(一 J S u b s创加 te .
2 o f re g u ıa r p o ıy g o n
A = ļ a p F o rm u ıa fo r a re a
o th e rw ıs e .
u n ıe s s yo u a re to ıd
th e n e a re s t te n th
fin a ı a n s w e rs to
s te p . R o u n d y
o u r
u n til t h e ıa s t
yo u a v o ıd ro u n d ın g
m o re a c c u ra te ıf
a n s w e r w ııı b e
ın g e n e ra ı, yo u r
S te p 3 F in d t h e a re a A o f t h e c o a s t e n
a = R S
ĺ o r A R Q S .
T o fın d R S , u s e t h e Py t h a g o re a n T h e o re m
◆
h a s s id e s , s o P =
_(J = c e n t i m e t e r s .
S te p 1 F ın d th e p e rim e te r P o f t h e c o a s te r. A n o c ta g o n
s o ıu t ıo n P
W h a t ıs t h e a re a o f t h e c o a s t e r ?
a ra d ıu s o f a b o u t 3 . 9 2 c e n tım e te rs .
o c ta g o n w it h 3 c e n t im e te r s id e s a n d
C o a s te r A w o o d e n c o a s t e r ıs a re g u la r
E x a m p \ e 2 F in d t h e a r e a o f a r e g u la r p o ıy g o n
A =一
,· · A =
一
'
,
a p o t h e m a a n d t h e p e rim e t e r P , s o
ıe n g th s is h a ıf th e p ro d u c t o f t h e
T h e a re a o f a re g u la r n - g o n w it h s ıd e
T H E O R E M ıı. ıı A R E A O F A R E G U U R p O LY G O NY o u r N o t e s
3 0 2 L e s s o n 1 1 . 6 ·
G ı o m e t ry
N o t e t a ıd ı ıg
O u l d e C op y
r ig
h t © M c D o ug
a ı L i t t e l l/ H o u g h to n M ifn in C o m p a n y ,
a n d a p o t h e m a = L M =
s = 2 M K = 2 ( ) =J ł K
T h e re g u la r n o n a g o n h a s s ıd e ıe n g th s
= M K
s in = c o s
M K
ra tıo s fo r rig h t A H L M .
is . T o f in d t h e ıe n g th s o f t h e le g s , u s e t r ig o n o m e t ric
A p o t h e m į iii b ıs e c ts t h e c e n t ra ı a n g le , s o m Z K L M
T h e m e a s u re o f c e n t ra l Z J L K is , o r .
/, K
i š
p e rım e t e r P a n d a re a A o f t h e n o n a g o n .
c ırc ıe w ıt h ra d ıu s 5 u n ıt s . F ın d t h e
A re g u la r n o n a g o n ıs ın s c rıb e d ın a
E x a m p \ e 3 m th e p e rim e te r a n d a re a o f a re g u la r U
to t h e n e a re s t s q u a re in c h .
( R
T
ls a b o u t 6 . 8 ın c h e s . F in d t h e a re a
T h e ra d iu s o f th e re g u la r p e n ta g o n in .2 .
m L K J F .
ın s c rib e d in O K . F ın d m Z F ıK / a n d
1 . ın t h e d ia g ra m , F G H I ıs a s qu a r e
G ų H
e c h e c lçp o fn t C o m p ıe t e t h e fo lıo w ın g e x e r c ıs e s .
y o u r N o te s
C o p y rig h t e M c D o u g a l u tte ıl/ H o u � h to n M iM in C o m p a n y . L e s s o n 1 1 . 6 ·
G e o m my
N o t ı * a k l ng
G ıı ıd · 1 0 3
r o r a o r s C h e c k p o in t E x . 3
Trig o n o m e try A n y o n e m e a s u re : E x a m p ıe 3 a n d
is 3 , 4 , o r 6
A n d th e v a ıu e o f n
r o r a o r s
A n y o n e m e a s u re : C h e c k p o in t E x . 3
Tria n g le s
S p e c ia l R ig h t
(å · ) 2
+ a2 _
r2
T h e o re m r a n d a , o r r a n d s C h e c kp
o i n t E j ( . 2
Py th a g o re a n T w o m e a s u re s : E x a m p le 2 a n d
Y o u c a n U S E
= i Y Xy
tW ı a s In . ' '
s id e le n g th s .
y o u m a y n e e d to firs t f in d t h e a p o t h e m a o r t h e
T o f in d t h e a re a o f a re g u ıa r w o n w it h ra d iu s r ,
H o m e w o r k
F ıN m N e N M H S ıN A R E a u u w N
e q u lıa te ra ı t rıa n g le in s c rib e d in O F .
3 . F in d t h e p e rim e te r a n d a re a o f t h e
e C h e c ¢qp o ï ııt C o m p ıe t e t h e fo ılo w ın g e x e r c ıs e .
y o u r N o te s