Polygons and Circles: Formulas and Properties for Class 10

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_apxm

1/28/2023

Geometry

Polygons and Circles

Subjects

Geometry

Circles

Constructing Regular Polygons Inscribed in Circles

Polygons and Circles: Formulas and Properties for Class 10

Name: Knowunity
Brand: Knowunity

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

293

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 = 2πr) and area (A = 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

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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/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.

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 (regular and irregular)
Circle components (radius, diameter, circumference)
The mathematical constant pi (π)

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

Polygons and Circles: Formulas and Properties for Class 10

_apxm

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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

293

Geometry

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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 = 2πr) and area (A = 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

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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/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.

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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 (regular and irregular)
Circle components (radius, diameter, circumference)
The mathematical constant pi (π)

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

Sign up to see the content. It's free!

Access to all documents

Improve your grades

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 (3 sides) to decagons (10 sides)
The formula for calculating the sum of interior angles: (n-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.

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Download in

Google Play

Download in

App Store

4.9+

Average App Rating

20 M

Students use Knowunity

#1

In Education App Charts in 17 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User