How to Find the Area of a Pentagon?

A five-sided closed polygon is known as a pentagon in geometry. There are different types of pentagons, such as regular, irregular, convex, or concave; however, the one that is most commonly used by students is a regular pentagon.

How to Find the Area of a Pentagon?

In this, all five sides and five angles are of equal measure. There are many concepts associated with pentagons, such as perimeter and area of pentagon. Let us take a further look into the different types of pentagons and how to find their areas.

Regular Pentagons

  • The sides and the angles are of equal measure
  • Each interior angle measures 108 degrees, while each exterior angle is 72 degrees.
  • It consists of five diagonals within the figure.
  • The sum of all internal angles of a pentagon is 540 degrees.

Irregular Pentagons

An irregular pentagon is one in which there are five sides; however, the length of the sides is not equal. There are two types of irregular pentagons.

  • Concave Pentagons: One of the interior angles is greater than 180 degrees. The vertices of a concave pentagon always point inwards.
  • Convex Pentagons: No internal angle can be greater than 180 degrees. In a convex pentagon, the vertices or points where the sides meet point outwards.

Area of a Pentagon

The area of a pentagon is defined as the region enclosed within the five boundaries. There are mainly two ways to find the area of a pentagon.

1. Application of Formula

To find the area of a regular polygon, you can use the following formula:

Area = 5/2 s a

where s is the length of the side and a is the length of the apothem. Apothem is a line that is drawn from the center of the pentagon to any side that hits it at a right angle.

If you do not know the length of the apothem, then you can also calculate the area by using the side length. The formula for the same is given below:

Area = ¼ √[5(5 + 2√5)] s² 

This formula can also be used to calculate the area of an irregular polygon. 

2. Triangular Method

When you have a regular pentagon, the area can be found by dividing the polygon into five triangles. You can draw a line from the center of the polygon to the vertices to form the triangles. The height of the triangle is given by the length of the apothem. It also divides the sides into two equal parts.

Area of the triangle = ½ base height

As there are five triangles, therefore, area of the pentagon = 5 area of a triangle.

Perimeter of a Pentagon

The perimeter of a pentagon can be found by adding the lengths of all the boundaries. If we have a pentagon with side lengths given by m, n, o, p, q, then the formula for the perimeter of a pentagon is given as:

Perimeter of a pentagon = sum of the lengths of the five sides = m + n + o + p + q

Conclusion

There are other concepts associated with a pentagon, such as how to construct it using a few given restrictions. It is best for a child to join an online educational institution such as Cuemath to gain the best quality of reliable knowledge. The math experts at Cuemath ensure kids have an enjoyable learning experience by using innovative teaching techniques and incorporating several interactive resources such as worksheets, workbooks, math puzzles, games, etc. Click here to know more about Cuemath, and I wish you all the best in your journey!