Chapter 5 - Geometry
Page 4 of 7
|Geometry - Geometric Polygons - Contents|
A polygon is a many sided enclosed geometric figure with straight edges represented on the two-dimensional Cartesian Plane. The term means many sided. A polygon has to have three or more straight sides with an equal number of interior angles making an enclosed figure with a continuous border. A regular polygon has equal sides and angles. The geometric area of any two-dimensional polygon is the amount of space that it encloses. Triangles are the simplest of the polygons easily recognizable as any enclosed figure with three straight sides. There are four common types, equilateral triangles are regular polygons where all sides and angles are equal, isosceles triangles has two equal sides, scalene triangles have all sides unequal and right triangles have one of their angles equal to a 90 degree right angle. The sum of the three angles in any enclosed triangle always adds up to 180 degrees. The area of any triangle is one-half the base times the height, where any of the sides can be used as the base. A quadrilateral is any enclosed polygonal figure with four straight sides. A rectangle is a quadrilateral with four right angles. A square is a regular polygon. It is a quadrilateral and a rectangle with equal angles and equal sides. The area of a rectangle is found by multiplying the base times the height. A parallelogram is a quadrilateral with both pair of opposite sides parallel to each other. A rhombus is a parallelogram with all sides equal. The sum of the angles in any quadrilateral is 360 degrees. Other polygons include pentagons, octagons, decagons which are 5 sided, 8 sided and 10 sided figures respectively. The area of all polygonal shapes and all well defined curvilinear shapes, including conic section, can be calculated by using geometry, trigonometry and calculus.
|Geometry - Geometric Polygons - Facts|
A right triangle cannot be an equilateral triangle since one angle is 90 degrees and they all add up to 180 degrees. A right triangle can be an isosceles triangle or a scalene triangle.
A square is also by definition a rectangle, a parallelogram, a rhombus, a quadrilateral, a polygon and a regular polygon.