Trojuholníky vidia všade okolo seba - v architektúre, umení aj... Show more
Matematika
Slovenský jazyk
AngličtinaSign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
72
•
Updated Mar 15, 2026
•
Jak vypočítat obvod a obsah trojúhelníka
1 / 8
Základné pojmy o trojuholníkoch
Trojuholník má tri strany (označujeme ich písmenami a, b, c), tri vrcholy (A, B, C) a tri vnútorné uhly. Každá strana leží oproti vrcholu s rovnakým písmenom - napríklad strana a leží oproti vrcholu A.
Výška trojuholníka je úsečka, ktorá ide z vrcholu kolmo na protiľahlú stranu. Každý trojuholník má tri výšky - v_a ide na stranu a, v_b na stranu b a v_c na stranu c. Základňa je tá strana, ku ktorej meriame výšku.
Podľa strán rozoznávame rovnostranný (všetky strany rovnaké), rovnoramenný (dve strany rovnaké) a rôznostranný trojuholník. Špeciálny je pravouhlý trojuholník s jedným 90° uhlom.
Tip: Vždy si nakresli obrázok! Pomôže ti to správne označiť strany a výšky.
Obvod trojuholníka
Obvod je vlastne dĺžka "okraja" trojuholníka - predstav si, že ideš po všetkých jeho stranách a meriaš, koľko prejdeš. Je to super jednoduché!
Stačí sčítať dĺžky všetkých troch strán: O = a + b + c. Ak máš trojuholník so stranami 5 cm, 7 cm a 6 cm, obvod je 5 + 7 + 6 = 18 cm.
Pre rovnostranný trojuholník sa vzorec zjednoduší na O = 3 × a (keďže všetky strany sú rovnaké). Pre rovnoramenný bude O = 2 × a + c (ak sú strany a a b rovnaké).
Pozor: Jednotky obvodu sú vždy dĺžkové - cm, m, km!
Obsah trojuholníka
Obsah je veľkosť plochy, ktorú trojuholník zaberá - predstav si, koľko farby by si potreboval na jeho vymaľovanie. Na výpočet potrebuješ poznať dĺžku jednej strany (základne) a výšku k nej.
Základný vzorec je: S = (základňa × výška) / 2. Môžeš použiť S = / 2, alebo S = / 2, alebo S = / 2 - výsledok bude vždy rovnaký!
Prečo delíme dvoma? Lebo trojuholník je presne polovica rovnobežníka s rovnakou základňou a výškou. Ak máš trojuholník so stranou 8 cm a výškou 5 cm, obsah je (8 × 5) / 2 = 20 cm².
Kľúčové: Výška musí byť vždy kolmá na základňu - tvoriť s ňou pravý uhol!
Špeciálny prípad - pravouhlý trojuholník
Pravouhlý trojuholník ti uľahčuje prácu! Jeho odvesny (strany pri pravom uhle) sú zároveň základňa a výška jedna k druhej. Nepotrebuješ hľadať žiadnu špeciálnu výšku.
Ak máš pravouhlý trojuholník s odvesnami 3 cm a 4 cm, obsah vypočítaš ako S = (3 × 4) / 2 = 6 cm². Prepona (najdlhšia strana) je 5 cm, takže obvod je 3 + 4 + 5 = 12 cm.
Toto ti ušetrí veľa času na teste! V pravouhlom trojuholníku sú dve strany automaticky základňa a výška.
Super tip: V pravouhlom trojuholníku: S = (odvesna₁ × odvesna₂) / 2
Praktické príklady a riešenia
Skúsme si to na konkrétnom príklade. Máš trojuholník so stranami a = 6 cm, b = 8 cm, c = 10 cm a výškou v_a = 7 cm.
Obvod: O = 6 + 8 + 10 = 24 cm. Obsah: S = (6 × 7) / 2 = 42 / 2 = 21 cm².
Pre rovnoramenný trojuholník so stranami 7 cm, 7 cm, 4 cm a výškou na základňu 6,7 cm: Obvod = 7 + 7 + 4 = 18 cm, obsah = (4 × 6,7) / 2 = 13,4 cm².
Nezabudni: Jednotky obsahu jsou plošné - cm², m²!
Dôležité tipy a časté chyby
Najčastejšie chyby, ktorým sa môžeš vyhnúť: Nezabúdaj deliť dvoma pri výpočte obsahu! Dávaj pozor na jednotky - obvod v cm, obsah v cm².
Výška a základňa musia patriť k sebe - ak používaš stranu a, musíš použiť výšku v_a. Nikdy nemiešaj rôzne strany s rôznymi výškami!
Vždy si over, či máš správnu výšku. V ostrouhlom trojuholníku je vo vnútri, v pravouhlom sú to odvesny, v tupouhlom môže byť aj vonku na predĺžení základne.
Na záver: Nakresli si obrázok, over si jednotky a nezabudni deliť obsah dvoma!
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
Most popular content
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
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
Jak vypočítat obvod a obsah trojúhelníka
Trojuholníky vidia všade okolo seba - v architektúre, umení aj prírode. Aby si ich dobre pochopil, musíš vedieť vypočítať ich obvod a obsah, čo sa ti zíde nielen na matike, ale aj v bežnom živote.
Základné pojmy o trojuholníkoch
Trojuholník má tri strany (označujeme ich písmenami a, b, c), tri vrcholy (A, B, C) a tri vnútorné uhly. Každá strana leží oproti vrcholu s rovnakým písmenom - napríklad strana a leží oproti vrcholu A.
Výška trojuholníka je úsečka, ktorá ide z vrcholu kolmo na protiľahlú stranu. Každý trojuholník má tri výšky - v_a ide na stranu a, v_b na stranu b a v_c na stranu c. Základňa je tá strana, ku ktorej meriame výšku.
Podľa strán rozoznávame rovnostranný (všetky strany rovnaké), rovnoramenný (dve strany rovnaké) a rôznostranný trojuholník. Špeciálny je pravouhlý trojuholník s jedným 90° uhlom.
Tip: Vždy si nakresli obrázok! Pomôže ti to správne označiť strany a výšky.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Obvod trojuholníka
Obvod je vlastne dĺžka "okraja" trojuholníka - predstav si, že ideš po všetkých jeho stranách a meriaš, koľko prejdeš. Je to super jednoduché!
Stačí sčítať dĺžky všetkých troch strán: O = a + b + c. Ak máš trojuholník so stranami 5 cm, 7 cm a 6 cm, obvod je 5 + 7 + 6 = 18 cm.
Pre rovnostranný trojuholník sa vzorec zjednoduší na O = 3 × a (keďže všetky strany sú rovnaké). Pre rovnoramenný bude O = 2 × a + c (ak sú strany a a b rovnaké).
Pozor: Jednotky obvodu sú vždy dĺžkové - cm, m, km!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Obsah trojuholníka
Obsah je veľkosť plochy, ktorú trojuholník zaberá - predstav si, koľko farby by si potreboval na jeho vymaľovanie. Na výpočet potrebuješ poznať dĺžku jednej strany (základne) a výšku k nej.
Základný vzorec je: S = (základňa × výška) / 2. Môžeš použiť S = / 2, alebo S = / 2, alebo S = / 2 - výsledok bude vždy rovnaký!
Prečo delíme dvoma? Lebo trojuholník je presne polovica rovnobežníka s rovnakou základňou a výškou. Ak máš trojuholník so stranou 8 cm a výškou 5 cm, obsah je (8 × 5) / 2 = 20 cm².
Kľúčové: Výška musí byť vždy kolmá na základňu - tvoriť s ňou pravý uhol!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Špeciálny prípad - pravouhlý trojuholník
Pravouhlý trojuholník ti uľahčuje prácu! Jeho odvesny (strany pri pravom uhle) sú zároveň základňa a výška jedna k druhej. Nepotrebuješ hľadať žiadnu špeciálnu výšku.
Ak máš pravouhlý trojuholník s odvesnami 3 cm a 4 cm, obsah vypočítaš ako S = (3 × 4) / 2 = 6 cm². Prepona (najdlhšia strana) je 5 cm, takže obvod je 3 + 4 + 5 = 12 cm.
Toto ti ušetrí veľa času na teste! V pravouhlom trojuholníku sú dve strany automaticky základňa a výška.
Super tip: V pravouhlom trojuholníku: S = (odvesna₁ × odvesna₂) / 2
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Praktické príklady a riešenia
Skúsme si to na konkrétnom príklade. Máš trojuholník so stranami a = 6 cm, b = 8 cm, c = 10 cm a výškou v_a = 7 cm.
Obvod: O = 6 + 8 + 10 = 24 cm. Obsah: S = (6 × 7) / 2 = 42 / 2 = 21 cm².
Pre rovnoramenný trojuholník so stranami 7 cm, 7 cm, 4 cm a výškou na základňu 6,7 cm: Obvod = 7 + 7 + 4 = 18 cm, obsah = (4 × 6,7) / 2 = 13,4 cm².
Nezabudni: Jednotky obsahu jsou plošné - cm², m²!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Dôležité tipy a časté chyby
Najčastejšie chyby, ktorým sa môžeš vyhnúť: Nezabúdaj deliť dvoma pri výpočte obsahu! Dávaj pozor na jednotky - obvod v cm, obsah v cm².
Výška a základňa musia patriť k sebe - ak používaš stranu a, musíš použiť výšku v_a. Nikdy nemiešaj rôzne strany s rôznymi výškami!
Vždy si over, či máš správnu výšku. V ostrouhlom trojuholníku je vo vnútri, v pravouhlom sú to odvesny, v tupouhlom môže byť aj vonku na predĺžení základne.
Na záver: Nakresli si obrázok, over si jednotky a nezabudni deliť obsah dvoma!
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.
2
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Practice Test ✓ Essay Outlines
Practice Test
Quiz
Flashcards
Essay
Most popular content in Matematika
Most popular content
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
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