Geometrijska telesa so vse okrog nas – od škatle za... Show more
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Updated Apr 10, 2026
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Razumevanje Geometrijskih Teles
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Uvod v geometrijska telesa
Predstavljaj si razliko med risbo kvadrata na papir in pravo kocko v rokah. Geometrijska telesa so tridimenzionalne oblike, ki jih lahko prijameš in držiš, ker imajo dolžino, širino IN višino.
Vsako geometrijsko telo sestavlja več mejnih ploskev (ravnih površin), ki se stikajo v robovih (črtah). Tam, kjer se srečajo trije ali več robov, nastane oglišče – to je "vogal" telesa.
Če geometrijsko telo "razgrnemo" kot darilo, dobimo mrežo telesa. To je kot da bi razrezali škatlo in jo razporedili po mizi. Površina nam pove, koliko papirja potrebujemo za ovijanje celega telesa, prostornina pa, koliko vode lahko vlijemo vanj.
💡 Pomni: Površina je "obleka" telesa (enota: cm²), prostornina pa "vsebina" telesa (enota: cm³)!
Kocka – popolno geometrijsko telo
Kocka je najlažje geometrijsko telo za razumevanje, ker je popolnoma simetrična. Sestavlja jo šest popolnoma enakih kvadratov, ima 12 enako dolgih robov (dolžina a) in 8 oglišč.
Obstaja kar 11 različnih mrež kocke, vendar vse vsebujejo 6 enakih kvadratov, ki se lahko pravilno zložijo v kocko. To je super za preverjanje na testih!
Površina kocke je preprosta: ker ima 6 enakih kvadratnih ploskev, samo pomnožimo ploščino enega kvadrata s 6. Formula je P = 6 × a².
Prostornina kocke je še lažja: pomnožimo rob sam s sabo trikrat. Formula je V = a³ (beremo "a na kub").
💡 Praktičen nasvet: Če imaš kocko z robom 2 cm, je njena površina 6 × 4 = 24 cm², prostornina pa 8 cm³!
Kvader – podolgovata kocka
Kvader je kot podolgovata škatla – ima še vedno 6 mejnih ploskev (pravokotnikov), 12 robov in 8 oglišč, vendar robovi niso vsi enako dolgi.
Označimo tri različne dolžine robov z a (dolžina), b (širina) in c (višina). Nasproti ležeče ploskve so vedno enake – to pomeni, da imamo 3 pare enakih pravokotnikov.
Površina kvadra je malo bolj zapletena, ker moramo sešteti ploščine vseh šestih ploskev: P = 2. Dvojka je tu zato, ker imamo od vsakega pravokotnika po dva.
Prostornina kvadra pa je preprosta: pomnožimo vse tri dimenzije skupaj. Formula je V = a × b × c.
💡 Pomni: Kvader je kot tri različne dimenzije, ki se množijo med sseboj za prostornino!
Praktični primeri z izračuni
Poglejmo si konkretna primera, ki jih boš srečal na testih!
Primer s kocko: Igralna kocka z robom 2 cm ima površino P = 6 × (2)² = 6 × 4 = 24 cm² in prostornino V = 2³ = 8 cm³.
Primer s kvadrom: Škatla za čevlje (30 cm × 20 cm × 10 cm) potrebuje P = 2(30×20 + 30×10 + 20×10) = 2(600 + 300 + 200) = 2200 cm² kartona. Njena prostornina je V = 30 × 20 × 10 = 6000 cm³.
Vedno najprej izpiši podatke, preveri enote in uporabi pravilno formulo. Pri površini dobiš kvadratne enote (cm²), pri prostornini pa kubične (cm³).
💡 Koristno za življenje: 1 liter = 1 dm³, torej kocka z robom 10 cm sprejme natanko 1 liter vode!
Hiter povzetek za uspeh na testu
Kocka: 6 enakih kvadratov, vsi robovi enaki (a)
- Površina: P = 6 × a²
- Prostornina: V = a³
Kvader: 6 pravokotnikov, 3 različne dimenzije (a, b, c)
- Površina: P = 2
- Prostornina: V = a × b × c
Ključne razlike: Površina je "obleka" (cm²), prostornina "vsebina" (cm³). Mreža je razgrnjeno telo – pri kocki 6 enakih kvadratov, pri kvadru 6 pravokotnikov v 3 parih.
Na testih pazi na enote in vedno preveri, ali imaš smiselne rezultate!
💡 Za odličen uspeh: Naredi si tabelo s formulami in jo uporabljaj, dokler se jih ne naučiš na pamet!
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Most popular content in Matematika
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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
Razumevanje Geometrijskih Teles
Geometrijska telesa so vse okrog nas – od škatle za čevlje do igralne kocke! To so 3D oblike, ki imajo dolžino, širino in višino ter zavzamejo pravi prostor. Naučili se boste izračunavati njihovo površino in prostornino.
Uvod v geometrijska telesa
Predstavljaj si razliko med risbo kvadrata na papir in pravo kocko v rokah. Geometrijska telesa so tridimenzionalne oblike, ki jih lahko prijameš in držiš, ker imajo dolžino, širino IN višino.
Vsako geometrijsko telo sestavlja več mejnih ploskev (ravnih površin), ki se stikajo v robovih (črtah). Tam, kjer se srečajo trije ali več robov, nastane oglišče – to je "vogal" telesa.
Če geometrijsko telo "razgrnemo" kot darilo, dobimo mrežo telesa. To je kot da bi razrezali škatlo in jo razporedili po mizi. Površina nam pove, koliko papirja potrebujemo za ovijanje celega telesa, prostornina pa, koliko vode lahko vlijemo vanj.
💡 Pomni: Površina je "obleka" telesa (enota: cm²), prostornina pa "vsebina" telesa (enota: cm³)!
Sign up to see the contentIt's free!
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Kocka – popolno geometrijsko telo
Kocka je najlažje geometrijsko telo za razumevanje, ker je popolnoma simetrična. Sestavlja jo šest popolnoma enakih kvadratov, ima 12 enako dolgih robov (dolžina a) in 8 oglišč.
Obstaja kar 11 različnih mrež kocke, vendar vse vsebujejo 6 enakih kvadratov, ki se lahko pravilno zložijo v kocko. To je super za preverjanje na testih!
Površina kocke je preprosta: ker ima 6 enakih kvadratnih ploskev, samo pomnožimo ploščino enega kvadrata s 6. Formula je P = 6 × a².
Prostornina kocke je še lažja: pomnožimo rob sam s sabo trikrat. Formula je V = a³ (beremo "a na kub").
💡 Praktičen nasvet: Če imaš kocko z robom 2 cm, je njena površina 6 × 4 = 24 cm², prostornina pa 8 cm³!
Sign up to see the contentIt's free!
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Join milions of students
Kvader – podolgovata kocka
Kvader je kot podolgovata škatla – ima še vedno 6 mejnih ploskev (pravokotnikov), 12 robov in 8 oglišč, vendar robovi niso vsi enako dolgi.
Označimo tri različne dolžine robov z a (dolžina), b (širina) in c (višina). Nasproti ležeče ploskve so vedno enake – to pomeni, da imamo 3 pare enakih pravokotnikov.
Površina kvadra je malo bolj zapletena, ker moramo sešteti ploščine vseh šestih ploskev: P = 2. Dvojka je tu zato, ker imamo od vsakega pravokotnika po dva.
Prostornina kvadra pa je preprosta: pomnožimo vse tri dimenzije skupaj. Formula je V = a × b × c.
💡 Pomni: Kvader je kot tri različne dimenzije, ki se množijo med sseboj za prostornino!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Praktični primeri z izračuni
Poglejmo si konkretna primera, ki jih boš srečal na testih!
Primer s kocko: Igralna kocka z robom 2 cm ima površino P = 6 × (2)² = 6 × 4 = 24 cm² in prostornino V = 2³ = 8 cm³.
Primer s kvadrom: Škatla za čevlje (30 cm × 20 cm × 10 cm) potrebuje P = 2(30×20 + 30×10 + 20×10) = 2(600 + 300 + 200) = 2200 cm² kartona. Njena prostornina je V = 30 × 20 × 10 = 6000 cm³.
Vedno najprej izpiši podatke, preveri enote in uporabi pravilno formulo. Pri površini dobiš kvadratne enote (cm²), pri prostornini pa kubične (cm³).
💡 Koristno za življenje: 1 liter = 1 dm³, torej kocka z robom 10 cm sprejme natanko 1 liter vode!
Sign up to see the contentIt's free!
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Improve your grades
Join milions of students
Hiter povzetek za uspeh na testu
Kocka: 6 enakih kvadratov, vsi robovi enaki (a)
- Površina: P = 6 × a²
- Prostornina: V = a³
Kvader: 6 pravokotnikov, 3 različne dimenzije (a, b, c)
- Površina: P = 2
- Prostornina: V = a × b × c
Ključne razlike: Površina je "obleka" (cm²), prostornina "vsebina" (cm³). Mreža je razgrnjeno telo – pri kocki 6 enakih kvadratov, pri kvadru 6 pravokotnikov v 3 parih.
Na testih pazi na enote in vedno preveri, ali imaš smiselne rezultate!
💡 Za odličen uspeh: Naredi si tabelo s formulami in jo uporabljaj, dokler se jih ne naučiš na pamet!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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4.6/5
App Store
4.7/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user