What is a Pentagon?
A ‘pentagon’ is a two-dimensional geometric shape. It is a type of polygon with 5 straight sides and 5 interior angles.
Types of Pentagon
Depending upon the angles, sides and vertices there are a few types of pentagons such as,
- Regular pentagon
A pentagon that has equal sides and equal interior angles is known as a regular pentagon.
- Irregular pentagon
A pentagon that does not have equal sides and unequal interior angles is called an irregular pentagon.
- Convex pentagon
A convex pentagon is a polygon that has interior angles less than 180 degrees and in which the vertices point outwards.
- Concave pentagon
A convex pentagon is defined as a pentagon which has 1 interior angle greater than 180 degrees.
Properties of a Pentagon
- The sum of all the interior angles of a pentagon is equal to 540 degrees.
- Each interior angle of a regular pentagon is 108 degrees and each exterior angle is 72 degrees.
- The pentagon has five diagonals and five vertices.
Solved Examples
Example 1: Find the value of x in the given figure?
Solution:
From the figure interior angles are – 68°, 121°, 103°, 85° and x°
As we know,
The sum of all the interior angles of the pentagon is equal to 540 degrees.
So,
68 + 121 + 103 + 85 + x = 540
⇒ 377 + x = 540
⇒ x = 540 – 377
⇒ x = 163
Hence, the value of the angle x is 163 degrees.
Example 2: Determine whether the following shape is a regular or an irregular pentagon.
Solution:
In the image we can observe that it is an irregular pentagon. This is because it does not have equal sides and equal angles.
Example 3: Calculate the perimeter of a regular pentagon with side 6 centimeters.
Solution:
Side of the regular pentagon = 6 cm
We know that,
Perimeter = sum of sides
= 6 + 6 + 6 + 6 + 6
= 30 cm
Hence, the perimeter of a regular pentagon with side 6 cm is 30 cm.
A pentagon that has all the sides and all the interior angles equal is defined as a regular pentagon. On the other hand, a pentagon which doesn’t have all the sides and all the interior angles equal is an irregular pentagon.
A convex pentagon is defined as a pentagon which has all the interior angles less than 180 degrees. A concave pentagon is defined as a pentagon which has one interior angle greater than 180 degrees.
The sum of the interior angles of a pentagon is 540 degrees.
A pentagon has five sides and five angles.
No, a pentagon is not similar to a parallelogram. A pentagon is a five sided polygon, while a parallelogram has just four sides.