Geometry - Polygons

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      Polygons are closed figures with many sides.  The sides are line segments.  Polygons are named and classified according to the number of sides and angles they contain. 

     Triangles, rectangles, squares, and pentagons are some well-known polygons.  A regular polygon is a polygon that has equal sides.

     Some familiar polygons are:

·         triangles

·         squares

·         rectangles

·         quadrilaterals

·         pentagons

·         hexagons

·         heptagons

·         octagons

·         nonagons

·         decagons

    Since polygons are closed figures with many sides, a shape that is not closed (i.e. an opening or a break in the lines) is not a polygon.  If a shape has any curved lines (for example, a circle or semicircle), it is not considered a polygon.

     A regular polygon is a polygon whose sides are the same length, such as a square or a hexagon.  A rectangle, for example, has sides of different lengths; therefore it would not be considered a regular polygon.

     Here is a list of some polygons and some of their characteristics:

·         Triangles are three-sided polygons whose angles measure the sum of 180°. 

·         Quadrilaterals are four-sided polygons whose angles measure the sum of 360°. 

·         Rectangles are four-sided polygons with 4 right angles.  Their angles measure the sum of 360° as well. 

·         Squares are four-sided polygons having equal-length sides meeting at right angles. The sum of the angles of a square is 360°.

·         A parallelogram is a four-sided polygon with two pairs of parallel sides. The sum of the angles of a parallelogram is 360°.

·         A rhombus is also a four-sided polygon having all four sides of equal length. The sum of the angles of a rhombus is 360°.

·         Trapezoids are four-sided polygons having exactly one pair of parallel sides. The two sides that are parallel are called the bases of the trapezoid. The sum of the angles of a trapezoid is 360°.

·         A pentagon is a five-sided polygon. The sum of the angles of a pentagon is 540°.

·         Hexagons are six-sided polygons. The sum of the angles of a hexagon is 720°.

·         A heptagon is a seven-sided polygon. The sum of the angles of a heptagon is 900°.

·         An octagon is an eight-sided polygon. The sum of the angles of an octagon is 1080°.

·         Nonagons are nine-sided polygon. The sum of the angles of a nonagon is 1260°.

·         A decagon is a ten-sided polygon. The sum of the angles of a decagon is 1440°.

     When studying polygons, we can measure their perimeter, area, angle measures, and the sum of their angle measures.  Polygons can be classified by number of sides, number of angles, number of vertices (corners), pairs of parallel sides, and equal side lengths. 

 For example, a triangle has:

Sides – 3

Angles – 3

Vertices - 3

Parallel Sides – 0

Equal Side Lengths – (it depends on the type of triangle)

     It is important for students to become familiar with the various polygons and their characteristics in order to be proficient at understanding geometry and measurement skills.

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Tutorgiant.com provides Polygon lessons with worksheets.

See some of the lessons in our video library.

ANGLES - Lesson (B) Angles in a Triangle (Grade 7)

ANGLES - Lesson (C) Angle Properties of Quadrilaterals (Grade 8)
SHAPES - Lesson (B) Identifying and Sorting 2-D Shapes (Grades 2-3)
SHAPES - Lesson (D) Introduction to Quadrilaterals (Grades 2-3)
SHAPES - Lesson (H) Quadrilaterals (Grades 4-5)
SHAPES - Lesson (I) Classifying 2-D Shapes (Grade 5)
SHAPES - Lesson (K) Measuring Angles in Polygons (Grades 4-6)
TRIANGLES - Lesson (A) Angles and Triangles (Grades 4-5)
TRIANGLES - Lesson (B) Triangles and Side Lengths (Grades 4-5)
AREA - Lesson (B) Area of a Rectangle (Grade 4)
AREA - Lesson (C) Area of a Parallelogram (Grades 7-8)
AREA - Lesson (E) Area of a Triangle (Grades 7-8)
AREA - Lesson (F) Area of Trapezoids (Grades 7-8)
AREA - Lesson (I) Area of Complex Shapes (Grades 7-8)
PERIMETER - Lesson (B) Perimeter of Rectangles (Grades 4-6)
PERIMETER - Lesson (C) Perimeter of Irregular Polygons (Grades 4-6)
PERIMETER - Lesson (D) Using a Formula to Find Perimeter (Grade 5)