7 Questions
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?
All angles are less than 180°
How is the area of a polygon calculated?
By dividing it into triangles and calculating the area of each triangle
What is the formula to calculate the area of a regular polygon?
Area = (number of sides × side length × apothem) / 2
What is the characteristic of a star polygon?
A polygon that is not convex, but can be formed by connecting non-adjacent vertices
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.
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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