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Dec 9, 2025
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Exploring Polygons and Quadrilaterals: Principles and Types
Knowunity Philippines
@knowunityphilippines
1 / 7
Understanding Polygons - Basic Definitions and Properties
Think of drawing a shape by connecting dots with straight lines until you get back to where you started - that's exactly what a polygon is! A polygon is simply a closed figure made up of three or more straight line segments called sides that meet at points called vertices.
To spot a polygon in the wild, check for three key things: it must be completely closed (you can trace around it without lifting your pencil), made only of straight lines (no curves allowed), and each side connects to exactly two other sides. It's like building with straight LEGO pieces - no curved bits allowed!
Polygons come in two main varieties: convex (where all corners point outward like a normal triangle) and concave (where at least one corner points inward, creating a "dent"). You'll also encounter regular polygons where everything's perfectly equal - same side lengths and same angles - versus irregular polygons where things can be a bit wonky.
Quick Check: The roof of a traditional Filipino bahay kubo forms a triangle (the simplest polygon), while your school's basketball court is rectangular .
Classification of Polygons by Number of Sides
Naming polygons is like having a secret code - each number of sides gets its own special name that mathematicians use worldwide. Once you know the pattern, you'll sound like a geometry expert!
The most common ones you'll encounter are triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides like the famous US building), and hexagons (6 sides like honeybee cells). Moving up, we get heptagons (7 sides), octagons (8 sides like stop signs), nonagons (9 sides), and decagons (10 sides).
For anything bigger than 10 sides, you can either learn the fancy names (like dodecagon for 12 sides) or just say "12-sided polygon" - both work perfectly fine. Most geometry problems stick to the simpler polygons anyway, so don't stress about memorizing every single name.
Fun Fact: The Philippine 20-peso coin is actually shaped like a 20-sided polygon (icosagon) - this unique design makes it easy to identify by touch alone!
Interior and Exterior Angles of Polygons
Here's where polygons get really clever - they follow predictable rules about their angles that work every single time. Understanding these angle formulas gives you superpowers for solving geometry problems quickly and confidently.
For interior angles (the angles inside the polygon), there's a magic formula: × 180° gives you the total sum, where n is the number of sides. Want each individual angle in a regular polygon? Just divide that total by the number of angles. It's that straightforward!
Exterior angles are even cooler - they always add up to exactly 360° no matter how many sides your polygon has. Whether it's a triangle or a 100-sided shape, those exterior angles will always total 360°. For regular polygons, each exterior angle equals 360° divided by the number of sides.
Try This: A regular octagon (like a stop sign) has interior angles of 135° each. Using the formula: (8-2) × 180° ÷ 8 = 135°. Pretty neat, right?
Special Quadrilaterals and Their Properties
Quadrilaterals are the celebrities of the polygon world - they're everywhere and each type has its own special talents. Learning their family relationships helps you understand which properties they inherit from each other.
Parallelograms are the parent family where opposite sides are parallel and equal, plus opposite angles match up. From here, we get rectangles (parallelograms with 90° angles), squares (rectangles with equal sides), and rhombuses (parallelograms with equal sides). Think of it like a family tree where each child gets all the parent's traits plus some extras.
Trapezoids are the rebels with exactly one pair of parallel sides, while kites have two pairs of equal adjacent sides. Each shape has unique properties that make them perfect for different real-world applications - rectangles for windows, squares for tiles, trapezoids for roof designs.
Real Connection: Filipino homes use rectangular windows because rectangles maximize space while maintaining structural strength, and traditional parol decorations often feature kite-shaped sections in their beautiful designs.
Problem-Solving with Polygon Properties
Ready to put your polygon knowledge to work? Problem-solving with polygons follows a simple four-step process that works for virtually any geometry question you'll encounter.
Start by identifying your polygon type and what information you're given, then figure out which property or formula applies. Substitute your known values into the right formula, solve for the unknown, and always check if your answer makes sense in the real world.
Here's a quick example: if a regular polygon has 40° exterior angles, how many sides does it have? Since exterior angles always sum to 360°, divide 360° by 40° to get 9 sides - that's a nonagon! The key is recognizing which formula fits your situation.
Pro Tip: When designing efficient layouts (like subdivisions in Metro Manila), urban planners often use hexagonal arrangements because hexagons fit together perfectly with no wasted space - geometry in action!
Practice Problems and Review
Time to flex those polygon muscles! Working through practice problems helps cement your understanding and builds confidence for tests and real-world applications.
Let's try a few: A heptagon's interior angles sum to (7-2) × 180° = 900°. If each interior angle of a regular polygon is 144°, then each exterior angle is 36°, giving us 360° ÷ 36° = 10 sides (a decagon). For a quadrilateral with angles of 85°, 95°, 75°, and x°, we know they must sum to 360°, so x = 105°.
Remember the big ideas: exterior angles always sum to 360°, regular polygons have equal everything, and quadrilaterals form a family hierarchy based on their properties. These relationships help you classify shapes and solve problems systematically.
Remember: Geometry isn't about memorizing formulas - it's about understanding how shapes relate to each other and using logical reasoning to solve problems. You've got this!
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 Math
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Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
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4.8/5
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 THE SCHOOLGPT. 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 THE SCHOOLGPT. 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
Exploring Polygons and Quadrilaterals: Principles and Types
Knowunity Philippines
@knowunityphilippines
Ever wondered why stop signs are octagonal or why honeybee cells are hexagonal? Understanding polygons - shapes made of straight sides - helps explain these everyday designs and gives you powerful tools for solving geometry problems.
Understanding Polygons - Basic Definitions and Properties
Think of drawing a shape by connecting dots with straight lines until you get back to where you started - that's exactly what a polygon is! A polygon is simply a closed figure made up of three or more straight line segments called sides that meet at points called vertices.
To spot a polygon in the wild, check for three key things: it must be completely closed (you can trace around it without lifting your pencil), made only of straight lines (no curves allowed), and each side connects to exactly two other sides. It's like building with straight LEGO pieces - no curved bits allowed!
Polygons come in two main varieties: convex (where all corners point outward like a normal triangle) and concave (where at least one corner points inward, creating a "dent"). You'll also encounter regular polygons where everything's perfectly equal - same side lengths and same angles - versus irregular polygons where things can be a bit wonky.
Quick Check: The roof of a traditional Filipino bahay kubo forms a triangle (the simplest polygon), while your school's basketball court is rectangular .
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Classification of Polygons by Number of Sides
Naming polygons is like having a secret code - each number of sides gets its own special name that mathematicians use worldwide. Once you know the pattern, you'll sound like a geometry expert!
The most common ones you'll encounter are triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides like the famous US building), and hexagons (6 sides like honeybee cells). Moving up, we get heptagons (7 sides), octagons (8 sides like stop signs), nonagons (9 sides), and decagons (10 sides).
For anything bigger than 10 sides, you can either learn the fancy names (like dodecagon for 12 sides) or just say "12-sided polygon" - both work perfectly fine. Most geometry problems stick to the simpler polygons anyway, so don't stress about memorizing every single name.
Fun Fact: The Philippine 20-peso coin is actually shaped like a 20-sided polygon (icosagon) - this unique design makes it easy to identify by touch alone!
Sign up to see the contentIt's free!
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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Interior and Exterior Angles of Polygons
Here's where polygons get really clever - they follow predictable rules about their angles that work every single time. Understanding these angle formulas gives you superpowers for solving geometry problems quickly and confidently.
For interior angles (the angles inside the polygon), there's a magic formula: × 180° gives you the total sum, where n is the number of sides. Want each individual angle in a regular polygon? Just divide that total by the number of angles. It's that straightforward!
Exterior angles are even cooler - they always add up to exactly 360° no matter how many sides your polygon has. Whether it's a triangle or a 100-sided shape, those exterior angles will always total 360°. For regular polygons, each exterior angle equals 360° divided by the number of sides.
Try This: A regular octagon (like a stop sign) has interior angles of 135° each. Using the formula: (8-2) × 180° ÷ 8 = 135°. Pretty neat, right?
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Special Quadrilaterals and Their Properties
Quadrilaterals are the celebrities of the polygon world - they're everywhere and each type has its own special talents. Learning their family relationships helps you understand which properties they inherit from each other.
Parallelograms are the parent family where opposite sides are parallel and equal, plus opposite angles match up. From here, we get rectangles (parallelograms with 90° angles), squares (rectangles with equal sides), and rhombuses (parallelograms with equal sides). Think of it like a family tree where each child gets all the parent's traits plus some extras.
Trapezoids are the rebels with exactly one pair of parallel sides, while kites have two pairs of equal adjacent sides. Each shape has unique properties that make them perfect for different real-world applications - rectangles for windows, squares for tiles, trapezoids for roof designs.
Real Connection: Filipino homes use rectangular windows because rectangles maximize space while maintaining structural strength, and traditional parol decorations often feature kite-shaped sections in their beautiful designs.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Problem-Solving with Polygon Properties
Ready to put your polygon knowledge to work? Problem-solving with polygons follows a simple four-step process that works for virtually any geometry question you'll encounter.
Start by identifying your polygon type and what information you're given, then figure out which property or formula applies. Substitute your known values into the right formula, solve for the unknown, and always check if your answer makes sense in the real world.
Here's a quick example: if a regular polygon has 40° exterior angles, how many sides does it have? Since exterior angles always sum to 360°, divide 360° by 40° to get 9 sides - that's a nonagon! The key is recognizing which formula fits your situation.
Pro Tip: When designing efficient layouts (like subdivisions in Metro Manila), urban planners often use hexagonal arrangements because hexagons fit together perfectly with no wasted space - geometry in action!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Practice Problems and Review
Time to flex those polygon muscles! Working through practice problems helps cement your understanding and builds confidence for tests and real-world applications.
Let's try a few: A heptagon's interior angles sum to (7-2) × 180° = 900°. If each interior angle of a regular polygon is 144°, then each exterior angle is 36°, giving us 360° ÷ 36° = 10 sides (a decagon). For a quadrilateral with angles of 85°, 95°, 75°, and x°, we know they must sum to 360°, so x = 105°.
Remember the big ideas: exterior angles always sum to 360°, regular polygons have equal everything, and quadrilaterals form a family hierarchy based on their properties. These relationships help you classify shapes and solve problems systematically.
Remember: Geometry isn't about memorizing formulas - it's about understanding how shapes relate to each other and using logical reasoning to solve problems. You've got this!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
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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4.9/5
App Store
4.8/5
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 THE SCHOOLGPT. 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 THE SCHOOLGPT. 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