Suci Wulandari – Hi Welcome to my blog. Hope you enjoy it

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V .Space oGe metry

: I T R A

P Polyhedra

s d r o

W Pronunciation Indonesian

e n i L w e k

S _{/skjuː laɪn /} Garis Bers liangan n

o r d e h y l o

P /ˌpɒl ˈɪhɛdrən / Bidang Banyak a

r d e h y l o

P /ˌpɒl ˈɪhɛdrə/ Bidang Banyak j(amak) e

c a

F /feɪs / S isi e

d i

S _{/ as ɪd/} S iis

e g d

E /ɛdʒ/ Rusuk

x e t r e

V _/vɜ:teks/ Titiksudut s

e c i t r e

V _{/vɜ:tɪs :iz/} Titiksudut-titiksudut e

d i

S -edge _{/ as ɪd ɛdʒ/} Rusuk tegak d

e s a

B -edge /beɪsd ɛdʒ/ Rusuk alas e

s a

B /beɪs/ Alas

l a r e t a

L Side _{/ˈlatərəl as ɪd/} Sis itegak m

s i r

P /ˈprɪz(ə)m/ Prisma m

s i r P t h g i

R _{/ ar ɪt}ˈprɪz(ə)m/ Prisma tegak m

s i r P e u q il b

O _{/ə’bl:ik ˈprɪz(ə)m/} Prisma miring e

m u l o

V /ˈvɒ jluːm / I si a

e r A e c a f r u

S /ˈsəːfɪs ˈɛːrɪə/ Luas Permukaan e

c a f r u S d e v r u

C k/ əːv d ˈsəːfɪs/ Se ilmut ( tabung/kerucut) t

h g i e

H _{/haɪ /t} Tinggi t

n a l

S Height _{/ ls ɑːn ath ɪt /} Panjang ruas garis Pelukis e

b u

C /kju:b/ Kubus d

i o b u

C /ˈkjuːbɔɪd / Balok e

c a

F -diagonal /feɪs dʌˈɪag(ə)n(ə l) / Diagona lbidang e

c a p

S -diagonal / esp ɪs dʌˈɪag(ə)n(əl) / Diagona lruang e

n a l P l a n o g a i

D /dʌˈɪag(ə)n(əl) epl ɪn / Bidang diagonal t

e

N /nɛt / Jaring-jaring d

i m a r y

P /ˈpɪrəmɪd / Limas d

il o S c i n o t a l

P /pləˈtɒnɪk ˈsɒlɪd / BangunpadatPlato n

o r d e h a r t e

T /ˌtɛtrəˈ hɛdrən / Tetrahedron n

o r d e h a x e

H /ˌhɛksəˈhɛdrən / Heksahedron n

o r d e h a c e d o

D /ˌdəʊdɛkəˈhɛdrən / Dodekahedron n

o r d e h a s o c

I /ˌʌɪkɒsəˈhɛdrən / Ikosahedron r

e d n il y

C /ˈsɪlɪndə/ Tabung e

n o

C /kəʊn / Kerucut e

r e h p

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Example:

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1 SkewLines are nonintersecting ilnes thatare notpara lle .l

.

2 A polyhedron is the union o fpolygona lregions such that a ifnite .

r o i r e t n i e h t n i s e l o h y n a t u o h t i w d e s o l c n e s i e c a p s f o n o i g e r

.

3 Parts of a Polyhedra

.

a The polygona lshapes that e r a n o r d e h y l o p e h t m r o f

s t i d e ll a

c faces/sides. .

b The ilne segments where s t i e r a t e e m s e c a f o w t

s e g d

e .

.

c A point where three or a s i t e e m s e g d e e r o m

x e t r e v

e c a f x

e t r e v

e g d e

a s a H

e l o

h N_clo_os t_ed

t o N

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4 Types of a Polyhedra s

m s i r P . A

¬ A prism si a polyhedron that has identica lpolygona lfaces r

e h t o h c a e e t i s o p p

o .

¬ The segments that connect base side and top side is ca lled

e d i

s -edges .The others i s ca lled based-edges.

¬ _{The opposite ,identica lside o fa prism are ca lled its bases.}

e h t d e ll a c e r a d n a s m a r g o l e ll a r a p e r a s e d i s r e h t o e h

T lateral

s e d i

s .

¬ _{I fthe latera lsides o fa prism are rectangles ,it is a right}

. m s i r

p I fnot, i t i s ca lled an oblique prism .

¬ When naming a prism we use two main descriptors . First , e

w n e h t , e u q il b o r o t h g i r s i t i r e h t e h w y a s e

w say what type

l a r e t a l s t i f o r e b m u n e h t r o s e s a b s ’ m s i r p e h t m r o f n o g y l o p f o

. s e d i s

¬ Genera lly ,the f ormula f or volume o fprismi s t

h g i e h s t i × e s a b s t i f o a e r A = V

t n a l s e h t t o n t h g i e h l a e r e h t s i a l u m r o f s i h t n i t h g i e h e h T

. t h g i e h

m s i r p l a n o g a t n e p t h g i r

5 t h g i

r -sidedprism oobbililqquuee4re-csitdaendguplrairsmprism

m s i r p t h g i

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1 Cube

e b u C a f o s t r a P

฀

6 lfat sides o f equa l s

e r a u q

s (ex :side ABCD )

฀

12 edges o fequal l engths )

B A e g d e : x e (

฀

8 vertices ( ex :pointA)

฀

12 f ace-diagonals ) F A e n il t n e m g e s : x e (

฀

4 space-diagonals ) G A e n il t n e m g e s : x e (

฀

6 diagona lplanes ) H G B A e d i s : x e (

e b u C a f o t e

N Formula for Volume and o

a e r A e c a f r u

S f a Cube

s i e b u c f o e m u l o v r o f a l u m r o f e h T

) e g d e f o h t g n e l( =

V 3

s i a e r a e c a f r u s r o f d n A

) e g d e f o h t g n e l( × 6 =

A 2

)

2 Cuboid ( Rectangular Prism)

฀

A rectangular prism has d il o s r a l u g n a t c e r 8

e l g n

a s , 12 edges , equa l . s r u o f n i l e ll a r a p d n a

฀

It is bounded by three t n e u r g n o c f o s r i a p

n i g n i y l s e l g n a t c e r

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o a e r A e c a f r u S d n a e m u l o V r o f a l u m r o

F f a Cuboid

d i o b u c f o s e g d e t n e r e ff i d e e r h t e h t e m a n n a c e w t a h t e s o p p u S f o e m u l o v r o f a l u m r o f e h t , n e h T . t h g i e h d n a , h t d i w , h t g n e l s a s i d i o b u c t h g i e h × h t d i w × h t g n e l = V s i a e r a e c a f r u s r o f d n A ]) t h g i e h × h t d i w ( + ) t h g i e h × h t g n e l( + ) h t d i w × h t g n e l( [ × 2 = A .

B Pyramid

¬ A pyramid is a three-dimensiona lsoild with one polygona l e h t f o s e c i t r e v e h t g n i t c e n n o c s t n e m g e s e n il h t i w d n a e s a b . e s a b e h t e v o b a e r e h w e m o s t n i o p e l g n i s a o t e s a b

¬ The latera lsides o fa pyramid are triangles . I fthey are t s e l e c s o s

i riangles ,then i t i s a right pyramid ,otherwise i t i s n

a oblique pyramid.

¬ _{Genera lly ,the f ormula f orvolume o fpyramid i s}

t h g i e h s t i × e s a b s t i f o a e r A × ) 3 / 1 ( = V e h t t o n t h g i e h l a e r e h t s n a e m o s l a a l u m r o f s i h t n i t h g i e h e h T . t h g i e h t n a l s d i m a r y p e r a u q s e u q il b

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5 The Platonic So ilds

r a l u g e r e l b i s s o p e v if y l n

O polyhedra exist .These ifve so ilds are S

D I L O S C I N O T A L P d e ll a c

r a l u g e R

n o r d e h y l o P

r e b m u N

s e d i S f o

h c a E

a s i e d i S

s n o g y l o P f o r e b m u N

x e t r e v a t a

n o r d e h a r t e

T 4 Triangle 3

n o r d e h a t c

O 8 Triangle 4

n o r d e h a s o c

I 2 0 Triangle 5

n o r d e h a x e

H 6 Square 3

n o r d e h a c e d o

D 1 2 Pentagon 3

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6 Cy ilnder

¬ A cy ilnder is a prismi nwhich the bases are circles orelilps.

¬ The volume o fa cyilnder is the area o fits base times its height

π = _r2_h

V

¬ _{The surface area o fa cyilnder i s} π

+ π

=_{2 r}2 _{2 rh}

A

s u i d a r s ’ e s a b f o h t g n e l = r

r e d n il y c f o t h g i e h = h

¬ A cyilnder can be right or obilque ,and cyilnders are named in the s

d i m a r y p d n a s m s i r p s a y a w e m a s

. 7 Cone

¬ A cone is ilke a pyramid but with a circular base instead o fa .

e s a b l a n o g y l o p

¬ The volume o fa cone is one-third the area o fits base times its :

t h g i e h

π = 1 _r2_h

V 3

¬ The surface area o fa cone i s base surface area +curved surface :

a e r a

ro A =πr2 +πr r2 +h2 s u i d a r s ’ e s a b f o h t g n e l = r

e n o c f o h t g i e h = h

π + π

= _r2 _rs

A

r e d n il y C r a l u c r i C t h g i R

A AnObilqueElilptica lCyilnder

e l c r i c a s i e s a b e h

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e n o c f o t h g i e h t n a l s = s

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8 Sphere

¬ Sphere is the mathematica lword f or “bal.l” It i s the set o fal l r e t n e c e h t d e ll a c t n i o p n e v i g a m o r f e c n a t s i d d e x if a e c a p s n i s t n i o p

. e r e h p s e h t f o

¬ The volume o fa sphere i s :_V = 4 rπ 3

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s e s i c r e x E s n o it s e u q e s e h t s r e w s n A . A .

1 Intersection o fthewalli n aclasscanbedescribedas_____________. .

2 Two planes i n aspace can ________________ or __________________ ,but cant’ . r e h t o h c a e _ _ _ _ _ _ _ _ _ _ _ _ .

3 What i sthenameo fobject thathas 6 vertices ,6 sides ,and 1 0 edges? .

4 I fa cuboid has edges whose lengths are 8 ,6 ,and 5 cm ,then its surface . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ s i a e r a .

5 A cyilndrica loi ltank can be if lled with 7,700 ilter gaso ilne .I fits base’s i l a i d a

r s70 cm ,then ifnd i ts height. .

6 Drawa neto fregularsquarepyramid and acone. .

7 Apyramid is i nscribed i n a cube .The top o fthe pyramid i s at the center o f s a h e b u c e h t f I . e b u c f o e d i s e s a b e h t s i e s a b s t i e li h w , e b u c f o e d i s p o t e h t . _ _ _ _ _ _ _ _ _ _ _ _ _ _ s i d i m a r y p e h t f o e m u l o v n e h t , m c 9 f o s e g d e .

8 A three dimensiona lobject that has 8 sides ,12 vertices ,and 1 8 _______ is . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ d e ll a c .

9 A cone is inscribed in a cyilnder .Their base side is equal ,whlie the top o f s a h r e d n il y c e h t f I . r e d n il y c f o p o t e h t f o r e t n e c e h t n i d e c a l p s i e n o c e h t e h t d n if , m c 4 2 f o t h g i e h d n a m c 7 f o i i d a

r curved surfaceareao fthecone.

. 0

1 What is the diameter o fthe sphere inscribed in a cube that is inscribed in ? 0 1 r e t e m a i d f o e r e h p s a . 1

1 The tota lsurface area o fa cube ,expressed in square centimeters ,is equa l i b u c n i d e s s e r p x e , e b u c e h t f o e m u l o v e h t o

t c centimeters .Compute the

a f o , s r e t e m i t n e c n i , h t g n e

l sideo fthesquare.

. 2

1 Two cy ilndrica lwater tank stand side by side .One has radius o f4 meters 3 f o s u i d a r a s a h r e h t o e h T . s r e t e m 5 . 2 1 f o h t p e d a o t r e t a w s n i a t n o c d n a u p s i r e t a W . y t p m e s i d n a s r e t e

m mped from the ifrst tank to the second

n u r p m u p e h t t s u m g n o l w o H . e t u n i m r e p s r e t e m c i b u c 0 1 f o e t a r a t a k n a t ? s k n a t h t o b n i e m a s e h t s i r e t a w e h t f o h t p e d e h t e r o f e b . 3

1 The pyramid ABCDE has a square base and al lfour triangular faces are e h T . l a r e t a li u q