Mensuration

Polygons

Have you heard about a polygon? What exactly comes to your mind when you think of a polygon? The tiles on which you walk are probably square or may be hexagonal which definitely means its a polygonal. From real-life objects, a STOP sign on the road side, a starfish or ball are all forms of a polygon. So let us try to find out what is a polygon.

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What is a Polygon?

In simple mathematics, a polygon can be any 2-dimensional shape that is formed with straight lines. Be it quadrilaterals or triangles and pentagons, these are all perfect examples of polygons. The interesting aspect is that the name of a polygon highlights the number of sides it possesses.

What is a Polygon

For example, a triangle has three sides, and a quadrilateral has four sides. So, any shape that can be drawn by connecting three straight lines is called a triangle, and any shape that can be drawn by connecting four straight lines is called a quadrilateral.

Types of Polygons

What is a Polygon

We know what is a polygon. But is there more to it? Yes! Of course, there is! The polygons are categorized into different types depending on the number of sides together with the extent of the angles.

Some of the prime categories of polygons include regular polygons, irregular polygons, concave polygons, convex polygons, quadrilateral polygons, pentagon polygons and so on. Some of the most well-known polygons are triangles, squares, rectangles, parallelograms, pentagons, rhombuses, hexagons etc.

Regular polygon

Considering a regular polygon, it is noted that all sides of the polygon are equal. Furthermore, all the interior angles remain equivalent.

Irregular polygon

These are those polygons that aren’t regular. Be it the sides or the angles, nothing is equal as compared to a regular polygon.

Concave polygon

A concave polygon is that under which at least one angle is recorded more than 180 degrees. Also, the vertices of a concave polygon are both inwards and outwards.

Convex polygon

The measure of the interior angle stays less than 180 degrees for a convex polygon. Such a polygon is the exact opposite of a concave polygon. Moreover, the vertices associated to a convex polygon are always outwards.

Quadrilateral polygon

Four-sided polygon or quadrilateral polygon is quite common. There are different versions of a quadrilateral polygon such as square, parallelogram and rectangle.

Pentagon polygon

Pentagon polygons are six-sided polygons. It is important to note that, the five sides of the polygon stay equal in length. A regular pentagon is a prime type of pentagon polygon.

Formulas

Area of a regular polygon = (1/2) N sin(360°/N) S2

where N is sides and S is the length from the centre to a corner.

Sum of the interior angles of a polygon = (N – 2) × 180°

The angle formed by two adjacent sides of the polygon are interior angles while angle formed by two adjacent sides outside the polygon are exterior angles.

Solved Examples For You

Q. I’m going to place a rope around the perimeter of our school playground that is in the shape of an octagon. The sides are 10m, 10m, 8m, 8m, 5m, 5m, 9m, 9m. How many metres of rope will be needed for the perimeter?

  1. 164 m
  2. 38m
  3. 64m
  4. 138m

Solution: C

Length of the rope required = perimeter of the school playground. The perimeter is the sum of all the sides of the polygon. Here the school playground is in the form of an octagon with the side as  10m, 10m, 8m, 8m, 5m, 5m, 9m, 9m

Perimeter =  10 + 10+ 8+ 8+ 5+ 5+ 9+ 9 = 64m

Length of the rope required = 64m

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