What is Pentagon? Area of a Pentagon Formula

What is Pentagon?

A Pentagon is the closed two-dimensional figure with five sides and five angles. So, this is also named as the five-sided shape or Regular Pentagon when all sides and angles are equal. As this is discussed already, the Pentagon is a closed figure. So, if angles or sides don’t meet each other then it cannot be named as the Pentagon.

Area of a Pentagon Formula

Pentagon may be regular, irregular, convex or concave. For the Regular Polygon, each of the interior angles is measured at 108-degrees and the exterior angle is measured at 72-degree. For the irregular Pentagon, sides are not the equal and angles are not aligned specifically. Next is convex Pentagon whose vertices point outwards while vertices of concave Pentagon point inwards. Imagine the roof of the house that is collapsed.

What are the Properties?

  • If a Regular Pentagon is divided into three equal triangles then the sum of the angles of a Triangle is 180-degrees. So, the sum of the interior angles of a Pentagon would be – 3*180°e. equal to 540° in mathematics.
  • For a Regular Pentagon, all sides and angles are same and congruent. If you want to know the measure of each individual interior angle divide the sum of angles i.e. 540 by 5. Here, each interior angle is measured at 108 °.
  • To calculate the central angle of a Pentagon, you need to draw a circle in the middle. This angle is measured as the 360 – degree and when it is divided by 5, it becomes 72 – degree each.

Area of a Pentagon Formula

A Pentagon is a five-sided shape in the Geometry. It may be simple or complex depends on the nature of the problem. Most of the common type of Pentagon that is followed during construction as well as a Regular Polygon having all equal sides and angles. Here, we will discuss the area of a Pentagon Formula. The area is defined as the space occupied within boundaries of the Pentagon.

The area of a Pentagon Formula in mathematics can be given as –

\[\ Area\;of\;a\;Pentagon\; = \frac{5}{2}sa \]
s is the side of the Pentagon.
a is the apothem length.


Once you put the values in the Formula, this is easy to calculate the area of a pentagon, In the same way, you can find out solutions for most complex problems are difficult to manage without proper technique in the real-life.

Question 1: Find the area of a pentagon of side 10 cm and apothem length 5 cm ?
s = 10 cm
a = 5 cm
area of a pentagon = 5/2 sa
area of a pentagon = 5/2 X 10 X 5 cm2
area of a pentagon = 5 X 5 X 5 cm2
= 125 cm2

Five-Sided Shape

A Pentagon is a five-sided shape. It is called the regular Pentagon if all sides are equal in length and equidistant from each other. For a regular shape, the placement of sides will create natural angles at the corner. With the line of symmetry, this is possible to divide the Pentagon into equal sections and shapes. But not all the pentagons are regular, if all five sides are not equal then they are termed as the irregular Polygons where few sides or angles will vary in length and it will not make the line of symmetry.