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Polygons and Circles: Formulas and Properties for Class 10

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_apxm

1/28/2023

Geometry

Polygons and Circles

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Geometry

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Circles

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Constructing Regular Polygons Inscribed in Circles

Polygons and Circles: Formulas and Properties for Class 10

This comprehensive guide explores polygons and circles, covering their definitions, properties, and formulas. It provides detailed explanations and examples to help students understand these geometric concepts.

Overall Summary:

This unit covers polygons and circles, two fundamental geometric shapes:

  • Polygons are classified by their number of sides, from triangles to decagons.
  • The sum of interior angles of a polygon can be calculated using the formula (n-2) × 180°.
  • Circles are defined by their center and radius, with formulas for circumference and area.
  • Key circle concepts include chords, sectors, and related calculations.
  • The guide includes examples and definitions of important geometric terms.
...

1/28/2023

298

UNIT 6: POLYGONS AND CIRCLES POLYGONS: POLYGONS CAN BE CLASSIFIED BY THE NUMBER OF SIDES THEY HAVE: TRIANGLES: 3 SIDES 180° QUADRILATERALS:

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Page 2: Circles and Their Properties

This page focuses on circles, their definitions, and formulas for calculating circumference and area. It also introduces the concept of chords in circles.

Definition: A circle is a shape formed by a set of points that are the same distance from a central point.

The page covers:

  • Definition of a circle using its center and radius
  • Formulas for calculating circumference C=2πrC = 2πr and area A=πr2A = πr² of a circle
  • Examples of circumference and area calculations for circles with given radii or diameters
  • Introduction to chords and bisectors in circles

Example: A circle with a radius of 5 units has a circumference of 31.42 units and an area of 78.54 square units.

Vocabulary:

  • Radius: The distance from the center of a circle to any point on the circle
  • Diameter: The distance across the circle, passing through the center
  • Chord: A line segment that connects two points on a circle
  • Bisector: The distance between the center of the circle and the midpoint of the chord
UNIT 6: POLYGONS AND CIRCLES POLYGONS: POLYGONS CAN BE CLASSIFIED BY THE NUMBER OF SIDES THEY HAVE: TRIANGLES: 3 SIDES 180° QUADRILATERALS:

View

Page 3: Sectors and Advanced Circle Concepts

This page delves deeper into circle concepts, focusing on sectors and their area calculations. It also provides more examples of chord and sector calculations.

Definition: A sector is a portion of a circle, defined by two radii and an arc.

The page covers:

  • Definition and explanation of sectors in circles
  • Formula for calculating the area of a sector: A = θ/360θ/360 × πr²
  • Examples of sector area calculations for different angles and circle sizes
  • Additional examples of chord bisector calculations

Example: A circle with a radius of 5 units and a sector with an angle of 90 degrees has an area of 19.63 square units.

Highlight: The area of a sector is proportional to the central angle that defines it, relative to the full circle.

UNIT 6: POLYGONS AND CIRCLES POLYGONS: POLYGONS CAN BE CLASSIFIED BY THE NUMBER OF SIDES THEY HAVE: TRIANGLES: 3 SIDES 180° QUADRILATERALS:

View

Page 4: Vocabulary and Key Concepts

This final page provides a comprehensive list of important vocabulary terms related to polygons and circles, serving as a quick reference for students.

Vocabulary:

  • Irregular polygon: A polygon with sides and angles not congruent
  • Circumference: The distance around the circle
  • Pi: A mathematical constant, represented by the symbol π, used in the calculation of the circumference of a circle

The page covers definitions for:

  • Polygon types regularandirregularregular and irregular
  • Circle components radius,diameter,circumferenceradius, diameter, circumference
  • The mathematical constant pi ππ

Highlight: Understanding these key terms is crucial for mastering the concepts of polygons and circles in geometry.

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Subjects

Geometry

Circles

Constructing Regular Polygons Inscribed in Circles

 

Geometry

•

298

•

Jan 28, 2023

•

4 pages

Polygons and Circles: Formulas and Properties for Class 10

user profile picture

_apxm

@_apxm

This comprehensive guide explores polygons and circles, covering their definitions, properties, and formulas. It provides detailed explanations and examples to help students understand these geometric concepts.

Overall Summary:

This unit covers polygons and circles, two fundamental geometric shapes:

  • Polygons are... Show more

UNIT 6: POLYGONS AND CIRCLES POLYGONS: POLYGONS CAN BE CLASSIFIED BY THE NUMBER OF SIDES THEY HAVE: TRIANGLES: 3 SIDES 180° QUADRILATERALS:

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Page 2: Circles and Their Properties

This page focuses on circles, their definitions, and formulas for calculating circumference and area. It also introduces the concept of chords in circles.

Definition: A circle is a shape formed by a set of points that are the same distance from a central point.

The page covers:

  • Definition of a circle using its center and radius
  • Formulas for calculating circumference C=2πrC = 2πr and area A=πr2A = πr² of a circle
  • Examples of circumference and area calculations for circles with given radii or diameters
  • Introduction to chords and bisectors in circles

Example: A circle with a radius of 5 units has a circumference of 31.42 units and an area of 78.54 square units.

Vocabulary:

  • Radius: The distance from the center of a circle to any point on the circle
  • Diameter: The distance across the circle, passing through the center
  • Chord: A line segment that connects two points on a circle
  • Bisector: The distance between the center of the circle and the midpoint of the chord
UNIT 6: POLYGONS AND CIRCLES POLYGONS: POLYGONS CAN BE CLASSIFIED BY THE NUMBER OF SIDES THEY HAVE: TRIANGLES: 3 SIDES 180° QUADRILATERALS:

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Page 3: Sectors and Advanced Circle Concepts

This page delves deeper into circle concepts, focusing on sectors and their area calculations. It also provides more examples of chord and sector calculations.

Definition: A sector is a portion of a circle, defined by two radii and an arc.

The page covers:

  • Definition and explanation of sectors in circles
  • Formula for calculating the area of a sector: A = θ/360θ/360 × πr²
  • Examples of sector area calculations for different angles and circle sizes
  • Additional examples of chord bisector calculations

Example: A circle with a radius of 5 units and a sector with an angle of 90 degrees has an area of 19.63 square units.

Highlight: The area of a sector is proportional to the central angle that defines it, relative to the full circle.

UNIT 6: POLYGONS AND CIRCLES POLYGONS: POLYGONS CAN BE CLASSIFIED BY THE NUMBER OF SIDES THEY HAVE: TRIANGLES: 3 SIDES 180° QUADRILATERALS:

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Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 4: Vocabulary and Key Concepts

This final page provides a comprehensive list of important vocabulary terms related to polygons and circles, serving as a quick reference for students.

Vocabulary:

  • Irregular polygon: A polygon with sides and angles not congruent
  • Circumference: The distance around the circle
  • Pi: A mathematical constant, represented by the symbol π, used in the calculation of the circumference of a circle

The page covers definitions for:

  • Polygon types regularandirregularregular and irregular
  • Circle components radius,diameter,circumferenceradius, diameter, circumference
  • The mathematical constant pi ππ

Highlight: Understanding these key terms is crucial for mastering the concepts of polygons and circles in geometry.

UNIT 6: POLYGONS AND CIRCLES POLYGONS: POLYGONS CAN BE CLASSIFIED BY THE NUMBER OF SIDES THEY HAVE: TRIANGLES: 3 SIDES 180° QUADRILATERALS:

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Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 1: Introduction to Polygons

This page introduces the concept of polygons and their classification based on the number of sides. It also explains how to calculate the sum of interior angles for various polygons.

Definition: A polygon is a closed figure made up of three or more line segments that form straight angles.

The page covers:

  • Classification of polygons from triangles 3sides3 sides to decagons 10sides10 sides
  • The formula for calculating the sum of interior angles: n−2n-2 × 180°
  • Examples of interior angle sums for different polygons

Example: A triangle has 3 sides and an interior angle sum of 180 degrees, while a square has 4 sides and an interior angle sum of 360 degrees.

Highlight: The sum of interior angles increases as the number of sides in a polygon increases, following a predictable pattern.

Vocabulary: Regular polygon - A polygon with all sides and angles congruent.

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Paul T

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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

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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