You can see that polygons can be regular or irregular, concave or convex, and simple or complex. Polygons can be studied and categorized in different ways. Polygon having a minimum of one interior angle greater than 180° is concave.Ĭomplex polygons have self-bisecting sides. Polygons with all interior angles measuring less than 180° are convex Polygons with congruent angles and sides are regular while all others are irregular. To be a polygon, the shape must be flat, circumscribed in space, and be created using only straight sides. Interior and exterior angles of a polygon are respectively, the inside and outside angles formed by the connecting sides of the polygon. Interior Angle of a hexagon = 180° − 60° = 120° Find out the Interior Angle of a Regular Octagon?Ī regular octagon consists of 8 sides, thus:Įxterior Angle of an octagon =\ Because the angle in this example is 135 degrees, the value of the supplementary angle is 45 degrees.ġ. This is the degree of each polygon's outer angle. To determine the exterior angle measure of a regular polygon, multiply the angle from Step 2 by 180 minus the degree. In a normal octagon, for example, each angle has a degree of 135:1. This is the degree of each of the polygon's angles. This adds up to 1,080.ĭivide the total calculated in Step 1 by the number of sides if the polygon is regular (all sides and angles are equal). The total of degrees for an octagon, for example, is (8-2) 180. Subtract 2 from the number of sides and multiply by 180 in this calculation). The total of all the inner angle degrees is (n - 2) 180. The polygon's sides are multiplied by the number of sides. In regular polygons, the degrees of the angles can be calculated, but this is not necessarily the case with non-regular polygons. Regular polygons have equal-length sides and equal-degree angles. Polygons can also be classed as regular or non-regular. Polygons are often classed based on the number of sides and the angles and sides' relative sizes. Polygons include triangles, trapezoids, and octagons, to name a few. The family of complex star-shaped polygons usually share the Greek number prefix and use the suffix -gram: pentagram, hexagram, heptagram, octagram, and so on.Ī polygon is a two-dimensional object that is closed and made up of three or more linked line segments. Most people can sketch a star on a sheet of paper very quickly, but some people label it a pentagram, complex polygon, or self-bisecting polygon. An example of a complex polygon is a classic star. Complex polygons, also known as self-intersecting polygons, contain sides that cross over each other. Simple polygons contain no self-intersecting sides. It will consist of two interior angles greater than 180°. Imagine a bowtie-shaped hexagon (6 sides). A concave polygon has a minimum of one angle greater than 180°. The dart is concave and the kite is convex.Įach interior angle of a convex polygon measures less than 180°. In geometrical math, you could have a 4-sided polygon that points outward in all directions, like a kite, or you could have similar four sides so two of them point inward, creating a dart. Square, Rectangle, Quadrilaterals- Parallelogram, Rhombus, Kite, DartĪ convex polygon closes in an interior space without appearing "dented." None of the interior angles points inward. For example, if the exterior angle is 60 degrees, then dividing 360 by 60 equals 6, which is the number of sides the polygon has. To calculate the number of sides of the polygon, divide 360 by the amount of the exterior angle. 360 divided by 15 = 24, which is the number of sides of the polygon in this case. If the inner angle was 165, for example, subtracting that from 180 would give you 15.ĭivide 360 by the angle difference and 180 degrees. Subtract the inside angle from 180 to get the outside angle. The internal and exterior angles, which are the inside and outside angles formed by the connecting sides of the polygon, may be used to compute the number of sides of a regular polygon. įor an Instance, A hexagon is a six-sided polygon, while a triangle is a three-sided one. The number of sides of a regular polygon can be computed with the help of interior and exterior angles. For example, a 3-sided polygon is a triangle, an 8 -sided polygon is an octagon, while an 11-sided polygon is called 11-gon or hendecagon. However, a polygon is considered regular when each of its sides measures equal in length. A polygon shape is any geometric shape that is classified by its number of sides and is enclosed by a number of straight sides.
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