Polygon

Let Us Learn About Polygons

Few names of polygons are as follows:

• Triangle or Trigon

This is a three-sided shape that having whole interior angle measurement as 180º.

• Quadrilateral or Tetragon

This is a four-sided shape that having whole inside angle measurement as 360º.

• Pentagon

This is a five-sided shape which contains the whole inside angle measurement as 540º.

The polygon is a closed path. The polygon has the different shapes. The shapes are depends on the number of sides. The Straight lines are form the polygon shapes. The polygons are having more number of straight lines to form the different polygons. Angles of the polygons are varied based on shape of the polygon.

The area of the regular polygon can be written as,

Area = S² N / 4 tan (pi / N).

Here, S = Length of any side, N = Number of side, Pi = 3.14.

Area of the Polygons

1) The given length of side:

Area Shape of polygon = S² N / 4 tan (Pi/N)

Here, S = Side length, N = Number of side, Pi = 3.14.

2) Given the radius(circum radius):

Area shape of polygon = (R² N sin (2Pi/N))/2.

Here, R = Radius of the polygon, N = Num

ber of side, Pi = 3.14.

3) Given the apothem (In radius):

Area Shape of polygon = A² N tan (Pi/N).

Here, A = Apothem length, N = Number of sides.

4) Given the apothem and Length of a side:

Area shape of polygon = A* P / 2.

Here, A = Apothem length, P = Perimeter.

More about Polygon:

Basic diagrammatic representation for polygon is as follows:

Polygon- A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others.

Regular Polygon- A regular polygon is a polygon whose sides are all the same length, and whose angles are all the same.

Quadrilateral- A four-sided polygon. The sum of the angles of a quadrilateral is 360^o.

Rectangle- A four-sided polygon having all right angles. The sum of the angles of a rectangle is 360^o.

Square- A four-sided polygon having equal-length sides meeting at right angles. The sum of the angles of a square is 360^o.

Parallelogram- A four-sided polygon with two pairs of parallel sides. The sum of the angles of a parallelogram is 360^o.

Rhombus- A four-sided polygon having all four sides of equal length. The sum of the angles of a rhombus is 360^o.

Trapezoid- A four-sided polygon having exactly one pair of parallel sides. The two sides that are parallel are called the bases of the trapezoid. The sum of the angles of a trapezoid is 360^o.

.Pentagon- A five-sided polygon. The sum of the angles of a pentagon is 540^o.

Hexagon- A six-sided polygon. The sum of the angles of a hexagon is 720^o.

Octagon- An eight-sided polygon. The sum of the angles of an octagon is 1080^o.

Nonagon- A nine-sided polygon. The sum of the angles of a nonagon is 1260^o.

Decagon- A ten-sided polygon. The sum of the angles of a decagon is 1440^o.

Convex- A figure is convex if every line segment drawn between any two points inside the figure lies entirely inside the figure. A figure that is not convex is called a concave figure.

Area of a square = side x side

= s x s

= s² sq units or units²

Area of a Rectangle = length x width

= l x w

= lw sq units or units²

Area of a Parallelogram= base x height

= b x h

= bh sq units or units²

Area of a Triangle = ½ x base x height

= ½ b h sq units or units²

Area of a Rhombus = base x height

= b x h

= bh sq units or unit²

Area of a Trapezoid = ½ (a+b)h sq units or units²

(Half of the sum of the lengths of the Parallel sides times height)