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Questions and Answers
What is the characteristic of a regular polygon?
What is the sum of interior angles of an n-sided polygon?
What is the formula to calculate the perimeter of a regular polygon?
What is the characteristic of a convex polygon?
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How is the area of a polygon calculated?
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What is the formula to calculate the area of a regular polygon?
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What is the characteristic of a star polygon?
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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.
