In geometry, a pentagon is a polygon with five sides. In a simple pentagon the sum of internal angles are about 540°. For example pentagram is a self-intersecting pentagon. Pentagon may be classified into regular and irregular. A pentagon that contains equal sides and equal internal angles are said to be regular pentagon otherwise the pentagon is irregular.pentagon
Number of Sides in a Pentagon:
The term penta indicates 5 .Hence the number of sides in a pentagon are 5 and the number of angles in a pentagon is 5.
A pentagon contains 712.694 million separate parallel lines.
Pentagon doesn’t have parallel lines.
Area of the pentagon = (perimeter of a polygon x apothem) ÷2
Where perimeter of a polygon = 5 x side.
The following are the other polygonal shapes with their sides.
Tetragon - 4 sides
Hexagon- 6 sides
Heptagon- 7 sides
Octagon- 8 sides
Nonagon Enneagon- 9 sides
Decagon-10 sides
Undecagon- 11 sides
Dodecagon- 12 sides
Properties of pentagon:
Number of diagonals:
Number of diagonals in a pentagon is 5
The number of different diagonals possible from all vertices.
Number of triangles:
Number of triangles in a pentagon is 10.
The number of triangles formed by sketching the diagonals from a given vertex.
Sum of interior angles:
Sum of interior angles of a pentagon is 540° in general 180(n–2) degrees.
Example Problem- Number of Sides in a Pentagon:
Example 1:
Find the perimeter of a regular pentagon whose side is 5ft.
Solution:’
Given that, side = 5ft.
For a regular pentagon all the sides are equal.
Therefore the perimeter of a regular pentagon = 5 x side.
= 5 x 5 =25ft.
Example 2:
Find area, from the apothem and the perimeter of a polygon is 4ft and 20ft.
Solution:
Given that, apothem = 4ft.
Perimeter = 20ft
Area of the pentagon = (perimeter of a polygon x apothem) ÷2
= (20 x 4) ÷2.
= 10 x 4.
= 40ft2
