Types of Polygons and Interior Angles
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Types of Polygons and Interior Angles

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Questions and Answers

What is the characteristic of a regular polygon?

All sides and angles are equal.

What is the sum of interior angles of an n-sided polygon?

(n-2) × 180°

What is the formula to calculate the perimeter of a regular polygon?

Perimeter = number of sides × side length

What is the characteristic of a convex polygon?

<p>All angles are less than 180°</p> Signup and view all the answers

How is the area of a polygon calculated?

<p>By dividing it into triangles and calculating the area of each triangle</p> Signup and view all the answers

What is the formula to calculate the area of a regular polygon?

<p>Area = (number of sides × side length × apothem) / 2</p> Signup and view all the answers

What is the characteristic of a star polygon?

<p>A polygon that is not convex, but can be formed by connecting non-adjacent vertices</p> Signup and view all the answers

Study Notes

Types of Polygons

  • Regular Polygons: All sides and angles are equal.
  • Irregular Polygons: Not all sides and angles are equal.
  • Convex Polygons: All angles are less than 180°.
  • Concave Polygons: At least one angle is more than 180°.
  • Star Polygons: A polygon that is not convex, but can be formed by connecting non-adjacent vertices.
  • Simple Polygons: A polygon that does not intersect itself.

Interior Angles of Polygons

  • The sum of interior angles of an n-sided polygon is (n-2) × 180°.
  • Each interior angle of a regular n-sided polygon is (n-2) × 180° / n.
  • Exterior angles of a polygon add up to 360°.

Perimeter of Polygons

  • The perimeter of a polygon is the sum of the lengths of all its sides.
  • The formula to calculate the perimeter of a regular polygon is: Perimeter = number of sides × side length.

Area of Polygons

  • The area of a polygon can be calculated by dividing it into triangles and calculating the area of each triangle.
  • The formula to calculate the area of a regular polygon is: Area = (number of sides × side length × apothem) / 2.
  • The apothem is the distance from the center of the polygon to one of its vertices.

Types of Polygons

  • A regular polygon is a polygon with all sides and angles equal.
  • An irregular polygon is a polygon where not all sides and angles are equal.
  • A convex polygon has all angles less than 180°.
  • A concave polygon has at least one angle greater than 180°.
  • A star polygon is a polygon that is not convex, formed by connecting non-adjacent vertices.
  • A simple polygon is a polygon that does not intersect itself.

Interior Angles of Polygons

  • The sum of interior angles of an n-sided polygon is (n-2) × 180°.
  • Each interior angle of a regular n-sided polygon is (n-2) × 180° / n.
  • The sum of exterior angles of a polygon is 360°.

Perimeter of Polygons

  • The perimeter of a polygon is the sum of the lengths of all its sides.
  • The formula to calculate the perimeter of a regular polygon is: Perimeter = number of sides × side length.

Area of Polygons

  • The area of a polygon can be calculated by dividing it into triangles and calculating the area of each triangle.
  • The formula to calculate the area of a regular polygon is: Area = (number of sides × side length × apothem) / 2.
  • The apothem is the distance from the center of the polygon to one of its vertices.

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Description

Explore the different types of polygons, including regular, irregular, convex, concave, star, and simple polygons, and learn about the sum of interior angles of an n-sided polygon.

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