We know that the polygons are those closed figures bounded by the straight line segments called as sides. The polygons are named according to the number of sides. They are also classified according to their sides and angles. You might have come across polygonal slabs fixed for the platforms or the floor of a building. These give attractive look for the surface where they are fixed. To fix certain number of polygonal tiles for the given area, we should know the area of each tile. It will be more convenient to calculate the number of tiles required for the given area, if we calculate the area of one tile. In this section let us see the methods of finding the area of different types of polygons, to enable us to solve the real life situations discussed above.





Convex Polygons: Polygons which have their interior angles acute, 90o or obtuse are called convex polygons.
Triangles, parallelograms, trapezoid, rectangle, square, kite area ll the convex polygons.
The following figures show some of the convex polygons.


Convex Polygons
Concave Polygons: Polygons which have at least one of their interior angles more than ( 180o ), reflex are called concave polygons.
The concave polygons will have its minimum number of sides four.
The following diagrams show some of the polygons which are concave.
The following figures show some of the concave polygons.


Concave Polygons
In the figure (a), the concave polygon is a quadrilateral which has one reflex angle.

In the figure ( b ), the concave polygon is a pentagon, which has one reflex angle.

In the figure ( c ), the concave polygon is a hexagon which has one reflex angle.

In the figure ( d ), the concave polygon is a hexagon with two reflex angles.
Equilateral Polygons: Polygons whose sides are congruent are called equilateral polygons.
Example: Equilateral Triangle, Square, rhombus, regular pentagon.

Equilateral Polygon

Equiangular Polygons: Polygons whose interior angles congruent are called equiangular polygons.
Example: Equiangular Triangle, Square, Rectangle.


Equiangular Triangle
Regular Polygons: Polygons whose sides are congruent and the interior angles are congruent are called regular polygons.
Example : Equilateral triangle, square, regular pentagon, regular hexagon etc.
Sum of the all the interior angle of a regular polygon = ( n - 2 ) 180o , where n is the number of sides.

Measure of each interior angle of a regular polygon =
$\frac{(n-2)180^{o}}{n}$, where n is the number of sides.

Irregular Polygons: Polygons whose sides or interior angles are unequal are called irregular polygons.
The following figure shows some of the regular and irregular polygons.
Sum of the all the interior angle of a regular polygon = ( n - 2 ) 180o , where n is the number of sides.
The measure of each interior angle will be different as the polygon is not regular.

Regular and Irregular Polygons