matematika-geometrija-8. razred-formule
DESCRIPTION
Formule iz geometrije za učenike osnovne škole 8. razred.TRANSCRIPT
![Page 1: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/1.jpg)
Zorana RaičevićZorana RaičevićGeomatrijska tela Geomatrijska tela
(formule)(formule)
Zorana RaičevićZorana RaičevićGeomatrijska tela Geomatrijska tela
(formule)(formule)Pokrenite prezentaciju na F5, a zatim ENTERPokrenite prezentaciju na F5, a zatim ENTER
Izaberite pitanje.Izaberite pitanje.
Klik miKlik mišem da pogledate odgovor.šem da pogledate odgovor.
Klik dole levo na , a zatim biraj novo pitanje. Klik dole levo na , a zatim biraj novo pitanje.
žuta-po 1 poenžuta-po 1 poen
zelena-po 2 poenazelena-po 2 poena
roza-po 3 poenaroza-po 3 poena
crveno/plavo-po 5 poenacrveno/plavo-po 5 poena1
![Page 2: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/2.jpg)
1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18
19 20 21 22 23 24 25 26 27
28 29 30 31 32 33 34 35 36
37 38 39 40 41 ** 42 43 44
45 46 47 48 49 50 51 52 53
54 55 56 57 58 59 60 61 62
63 64 65 66 67 68 69 70 71
![Page 3: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/3.jpg)
3
2ad
Dijagonala kvadrata stranice a
![Page 4: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/4.jpg)
4
2
3ah
Visina jednakostraničnog trougla stranice a
![Page 5: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/5.jpg)
5
2aP
aO 4
Površina i obim kvadrata stranice a
![Page 6: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/6.jpg)
6
4
36
2aP
aO 6
Površina i obim šestougla stranice a
![Page 7: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/7.jpg)
7
4
32aP
aO 3
Površina i obim jednakostraničnog trougla stranice a
![Page 8: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/8.jpg)
8
MBP
HBV
Površina i zapremina prizme
![Page 9: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/9.jpg)
9
2rP
rO 2
Površina i obim kruga poluprečnika r
![Page 10: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/10.jpg)
10
MBP
3
HBV
Površina i zapremina piramide
![Page 11: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/11.jpg)
11
MBP
HBV
Površina i zapremina valjka
![Page 12: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/12.jpg)
12
cmd 26
Dijagonala kvadrata stranice a=6cm
![Page 13: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/13.jpg)
13
cmh 23
Visina jednakostraničnog
trougla stranice a=6cm
![Page 14: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/14.jpg)
14
29cmP
cmO 12
Površina i obim kvadrata stranice
a=3cm
![Page 15: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/15.jpg)
15
2354 cmP 236cmO
Površina i obim šestougla stranice
a=6cm
![Page 16: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/16.jpg)
16
239 cmP
cmO 18
Površina i obim jednakostraničnog
trougla stranice a=6cm
![Page 17: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/17.jpg)
17
Površina kruga poluprečnika 5cm
225 cmP
![Page 18: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/18.jpg)
182
dro
Poluprečnik opisane kružnice oko
kvadrata dijagonale d
![Page 19: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/19.jpg)
19
2
aru
Poluprečnik upisane kružnice u kvadrat
stranice a
![Page 20: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/20.jpg)
202
2aro
Poluprečnik opisane kružnice oko
kvadrata stranice a
![Page 21: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/21.jpg)
216
3aru
Poluprečnik upisane kružnice u
jednakostranični trougao stranice a
![Page 22: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/22.jpg)
223
hru
Poluprečnik upisane kružnice u
jednakostranični trougao visine h
![Page 23: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/23.jpg)
233
3aro
Poluprečnik opisane kružnice oko
jednakostraničnog trougla stranice a
![Page 24: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/24.jpg)
243
2hro
Poluprečnik opisane kružnice oko
jednakostraničnog trougla visine h
![Page 25: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/25.jpg)
25
aD 2
Velika dijagonala šestougla stranice a
![Page 26: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/26.jpg)
26
2
3aru
Poluprečnik upisane kružnice u šestougao
stranice a
![Page 27: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/27.jpg)
27
3ad
Mala dijagonala šestougla stranice a
![Page 28: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/28.jpg)
28
aro
Poluprečnik opisane kružnice oko
šestougla stranice a
![Page 29: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/29.jpg)
29
2
2
2
12
22
dda
Stranica romba, ako su poznate dijagonale.
![Page 30: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/30.jpg)
30
0360
2 r
l
Dužina luka koji odgovara centralnom
uglu
![Page 31: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/31.jpg)
31
0
2
360
r
Pi
Površina isečka, koji odgovara centralnom
uglu
![Page 32: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/32.jpg)
32
HrM 2
Omotač valjka, ako je poznat poluprečnik r i
visina H
![Page 33: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/33.jpg)
33
221 dd
P
haP
Površina romba (na dva načina)
![Page 34: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/34.jpg)
34
2aB 4
32aB
4
36
2aB
Površina baze pravilne 3,4,6-strane
prizme
![Page 35: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/35.jpg)
35
222
2
a
sh
Apotema četvorostrane piramide, ako je poznata osnovna ivica a i bočna
ivica s
![Page 36: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/36.jpg)
36
222
2
a
sh
Apotema trostrane piramide, ako je poznata osnovna ivica a i bočna
ivica s
![Page 37: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/37.jpg)
37
222
2
a
sh
Apotema šestostrane piramide, ako je poznata osnovna ivica a i bočna
ivica s
![Page 38: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/38.jpg)
38
2
22
6
3
a
hH
Visina trostrane piramide, ako je poznata
apotema h i osnovna ivica a
![Page 39: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/39.jpg)
39
2
22
2
3
a
hH
Visina šestostrane piramide, ako je poznata
apotema h i osnovna ivica a
![Page 40: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/40.jpg)
40
222
2
a
hH
Visina četvorostrane piramide, ako je poznata
apotema h i osnovna ivica a
![Page 41: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/41.jpg)
41
2
22
3
3
a
sH
Visina trostrane piramide, ako je poznata bočna ivica s
i osnovna ivica a
![Page 42: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/42.jpg)
42
2
22
2
2
a
sH
Visina četvorostrane piramide, ako je poznata bočna ivica s i osnovna
ivica a
![Page 43: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/43.jpg)
43
222 asH
Visina šestostrane piramide, ako je poznata bočna ivica s i osnovna
ivica a
![Page 44: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/44.jpg)
44
300
a
b
c
Odredi strance b i c pravouglog trougla, ako je
kateta b=6cm
cmc
cmb
cma
12
6
36
![Page 45: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/45.jpg)
45
450
a
b
c
Odredi strance b i c pravouglog trougla, ako je
kateta a=6cm
cmc
cmb
cma
26
6
6
![Page 46: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/46.jpg)
46
600
a
b
c
Odredi strance b i c pravouglog trougla, ako je
kateta a=3cm
cmc
cmb
cma
16
32
3
![Page 47: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/47.jpg)
47
300
a
b
c
Odredi strance a i b pravouglog trougla, ako je
hipotenuza c=12cm
cmc
cmb
cma
12
6
36
![Page 48: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/48.jpg)
48
600
a
b
c
Odredi strance a i b pravouglog trougla, ako je
hipotenuza c=12cm
cmc
cmb
cma
12
36
24
![Page 49: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/49.jpg)
49
450
a
b
c
Odredi strance a i b pravouglog trougla, ako je
hipotenuza c=12cm
cmc
cmb
cma
12
26
26
![Page 50: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/50.jpg)
50
300
a
b
c
Odredi površinu pravouglog trougla, ako je stranica
cma 36
2318 cmP
![Page 51: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/51.jpg)
51
cmro 4
Poluprečnik opisane kružnice oko
kvadrata dijagonale 8cm
![Page 52: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/52.jpg)
52
cmru 4
Poluprečnik upisane kružnice u kvadrat
stranice 8cm
![Page 53: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/53.jpg)
53
cmro 2
Poluprečnik opisane kružnice oko kvadrata
stranice cm22
![Page 54: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/54.jpg)
54
cmru 2
Poluprečnik upisane kružnice u
jednakostranični trougao stranice cm34
![Page 55: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/55.jpg)
55
cmru 4
Poluprečnik upisane kružnice u
jednakostranični trougao visine h=12cm
![Page 56: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/56.jpg)
56
cmro 6
Poluprečnik opisane kružnice oko
jednakostraničnog trougla stranice cma 36
![Page 57: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/57.jpg)
57
cmro 8
Poluprečnik opisane kružnice oko
jednakostraničnog trougla visine
h=12cm
![Page 58: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/58.jpg)
58
cmD 30
Velika dijagonala šestougla stranice
a=15cm
![Page 59: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/59.jpg)
59
cmru 33
Poluprečnik upisane kružnice u šestougao
stranice a=6cm
![Page 60: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/60.jpg)
60
cmd 64
Mala dijagonala šestougla stranice
cma 24
![Page 61: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/61.jpg)
61a
b
c
Površina pravouglog trougla, čije su katete a i b,
a hipotenuza c.
2
baP
![Page 62: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/62.jpg)
62
Omotač pravilne trostrane piramide, ako je poznata osnovna ivica i apotema.
23
haM
![Page 63: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/63.jpg)
63
Omotač pravilne četvorostrane prizme
aHM 4
![Page 64: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/64.jpg)
64
Omotač pravilne šestostrane piramide.
26
haM
![Page 65: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/65.jpg)
65
Omotač pravilne šestostrane prizme
aHM 6
![Page 66: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/66.jpg)
66
Obim i površina pravougaonika
baP
baO
22
![Page 67: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/67.jpg)
67
Baza valjka, pouprečnika a i visine H
2rB
![Page 68: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/68.jpg)
68
Dijagonala pravougaonika stranica a i b
222 bad
![Page 69: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/69.jpg)
69
Površina trapeza
hba
P
2
![Page 70: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/70.jpg)
70
Površina kružnog isečka, ako je centralni ugao 300 , a
poluprečnik kruga 6cm
23 cmP
![Page 71: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/71.jpg)
71
Površina kocke ivice 4cm
296cmP
![Page 72: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/72.jpg)
72
Zapremina kocke ivice a
3aV
![Page 73: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/73.jpg)
73
Koliko puta je zapremina šestostrane prizme veća od
zapremine šestostrane piramide, ako su im
osnovne ivice 2cm, a visine po 10cm?PUTATRI
![Page 74: Matematika-geometrija-8. razred-formule](https://reader036.vdocuments.net/reader036/viewer/2022081413/5493aaa4b479594c4d8b48a6/html5/thumbnails/74.jpg)
74
Odredi r0 pravouglog trougla čije su katete 6cm i
8cm
ro=5cm