Regular polygons:
When each side and angles of any polygon are similar, then it is said to be a regular polygon. A regular polygon is one with its entire sides similar and each of its angles similar, for instance: A regular polygon with 3 surfaces is said to be equilateral triangle.
Irregular Polygons:
When angles of the any polygon are not the same, then it is called as irregular polygon.
Regular Irregular Polygons-angles of Regular Polygons:
The regular polygons’ angle is grouped into two types. They are
Exterior angle
Interior angle
Interior angle of Regular Polygons:
Angle of regular polygons = [(n - 2) / n] × 180°
where n =number of sides.
Example 1:
Octagon is an eight sided polygon
Regular Polygons’ Interior Angle = [(n - 2) / n] × 180°
Here n = 8 for octagon
So the interior angle of an octagon = [(8 – 2)/ 8] * 180°
= (3 / 4) * 180°
Interior angle of octagon = 540° / 4 = 135°
Exterior angle of Regular Polygons:
360° is the exterior angle of polygons. Hence the exterior angle can be estimated by the formula,
Regular Polygons’ Exterior angle = 360° / n
where n is the number of sides.
Example 2:
For Pentagon, n = 5
So the exterior angle of a pentagon = 360 / 5 = 72°.
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Regular Irregular Polygons-area of Irregular Polygons:
The steps for determining the area of irregular polygon are,
Convert every vertex into co-ordinate in graph.
Take any line segment and down to the x - axis.
Compute the average of two altitudes.
Compute the difference of two widths.
Multiply altitude with width.
Go over steps 2 to 5 until manipulating every line segment.
Then add all the areas of every line segment.
So, we will result in area of irregular shape.
Symmetry for Irregular Polygon:
Since the irregular polygons do not have equal angles, they do not posses line of symmetry..
