Polygons are two-dimensional shapes with straight sides. Learn about convex and concave polygons, distinguish regular from irregular ones, and understand how to calculate their areas and angles. Regular polygons have equal sides and angles, with unique geometric properties such as circumradius and apothem, essential for various calculations.
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Polygons are two-dimensional figures composed of straight line segments connected to form a closed shape
Edges
Edges are the straight line segments that make up the sides of a polygon
Vertices
Vertices are the points where two edges meet in a polygon
Polygons can be classified based on the number of sides they possess, such as triangles, pentagons, and hexagons
Convex polygons have no angles greater than 180° and all line segments drawn inside the shape will not extend outside, while concave polygons have at least one angle greater than 180° and at least one line segment that passes outside the shape
Convex polygons can be regular or irregular, while concave polygons are often irregular but can also be regular in certain cases
Regular star-shaped polygons are a type of concave polygon with equal angles and sides
Regular polygons have equal angles and sides, as well as equal diagonals from a single vertex
Symmetry
Regular polygons have symmetry in their angles and diagonals
Circles
Regular polygons are associated with two significant circles: the circumcircle, which passes through all vertices, and the incircle, which is tangent to each side at its midpoint
The area of a regular polygon can be calculated by dividing it into isosceles triangles and using the formula for the area of a triangle, while the number of diagonals can be found using a specific formula
Understanding the properties of regular polygons is crucial in geometry and has practical applications in fields such as architecture, engineering, and graphic design
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Polygons can be categorized as ______ or ______, and also as regular or irregular.
convex
concave
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Convex polygon internal angles
All internal angles less than 180°.
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Line segment within convex polygons
Stays inside polygon, doesn't extend outside.
