Most of you are familiar with the basic geometric shapes that surround us, like squares, kites, rectangles, circles, and so on. However, did you know that the name changes as the number of edges increases? The Pentagon is one of those intriguing shapes.
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What is a Pentagon?
A pentagon is a polygon with five sides, one more than a rectangle. A pentagon can be formed by connecting straight lines at different angles on a flat surface. The definition is derived from a Greek term that refers to a shape with 5 distinct sides, where Penta represents five and gon represents an angle. Pentagons are common geometric shapes used by architects to design houses, buildings, and other structures, and there are many natural examples of pentagons. A solid knowledge of shapes is required to fully comprehend how to apply shapes in geometry in practical settings.
Parts of a Pentagon Shape
- Side: It is one of the five line segments that form this shape. There are a total of five sides in this shape. In the image, the line segment ‘a’ shows one of the 5 pentagon-shaped sides.
- Vertex: The vertex is the point at which two sides of a shape intersect. In layman’s terms, it’s referred to as a corner. When you look at the page of your laptop, for example, you will notice that it has 4 corners or 4 vertices that shape a 90° angle. The 5 vertices of this shape are shown in the image above as A, B, C, D, and E.
- Diagonal: A line connecting two non-adjacent vertices. The diagonal is formed by connecting any 2 non-adjacent corners or vertices of a 2D figure with a straight line. In the picture, the diagonal is indicated by the letter “d” for reference.
- Interior angle: The angle created on the inside of a shape by 2 adjacent sides. In a closed two-dimensional figure, two different types of angles are formed when two straight lines cross or intersect. An internal angle is an angle that exists within the figure. Interior angles are indicated in the image above.
- Exterior angle: The angle created on the outside of a shape by 2 adjacent sides. The external angle is the angle measured on a specific vertex but on the outside. The exterior angles are shown in the above image.
Types of Pentagon
The pentagon, like all other polygons such as triangles and quadrilaterals (rectangles and squares,…), is a polygon with 5 sides and 5 angles. Pentagon shapes are divided into the following types based on their sides, angles, and vertices:
Regular Pentagon: Include 5 equal-length sides, 5 interior angles of 108° each, and 5 exterior angles of 72° each. As a result, a regular pentagon is both equilateral (it has 5 equal sides) and equiangular (including 5 angles of equal measure). Drawing diagonal lines between the nonadjacent vertices of a regular pentagon yields the pentagram star shape. There are 5 lines of symmetry in a regular pentagon.
- Irregular Pentagon: Has no specific angles because all sides and angles are not equal.
- Convex Pentagon: All vertices point outward, resulting in angles smaller than 180°. Therefore, a convex pentagon can also be regular.
- Concave Pentagon: A concave Pentagon has at least 1 vertex pointing inwards with an angle greater than 180°. As a result, all concave pentagons are irregular.
- Properties of a Pentagon
A pentagon has several interesting properties, including the following:
- The total value of the interior angle measured in a pentagon equals 540 degrees.
- A regular pentagon is one in which all of its sides are the same length and all of its angles are the same measure. It is otherwise an irregular pentagon.
- The interior angle of a regular pentagon is always 108 degrees, while the exterior angle of a regular pentagon is always 72 degrees.
- An equilateral pentagon has 5 sides that are all the same length.
- The total value of the interior angles in a rectangular pentagon is 540 degrees.
What is the Pentagon’s Area?
The area of a regular pentagon with a specific side and apothem length (the line from the center of the pentagon to a side that meets the side at a right angle, i.e., at 90 degrees) is calculated as follows:
Pentagon Area = A = (5/2) * Side Length * Apothem Sq Units
A regular pentagon’s area could be determined by dividing it into 5 equal triangles.
We already understand that the formula for determining the area of a triangle is ½ * Base * Height. As a result, we can calculate the area of a regular pentagon as :
5 * the Area of a triangle.
What is the Pentagon’s Perimeter?
Because all of the sides of a regular pentagon are the same length, the formula for calculating a pentagon’s perimeter or circumference is as follows:
Perimeter = P = 5a Units, where ‘a’ is the length of the pentagon’s side.
For other pentagons, the perimeter is the sum of all side’s lengths.
Real examples of Pentagons
You will undoubtedly come across a pentagon shape if you look around. There are numerous real-life examples of pentagons, whether they are irregular pentagons with various different side lengths or regular pentagons with equal sides and equal angles:
- The iconic United States Department of Defense building in Washington, D.C. (The Pentagon structure)
- A baseball field’s home plate
- School crossing signs
- A soccer ball’s sections
- Echinoderm shapes, such as sea stars
- A sea urchin’s endoskeleton
How do you make a five-sided shape for your kids?
One of the most effective ways to teach kids about geometric shapes or to help them memorize is to assist them in creating their own. Here are some simple steps you can take to make a regular 5-sided shape with just a strip of paper:
- Make a long paper strip. If you want a regular pentagon, ensure it’s the same width all the way around. The color can be any color you want. To make it even more enjoyable, allow kids to choose their favorite.
- The next step is to tie a pretzel-like knot with the paper.
- Tighten the knot while holding the paper flat. Take care not to break it.
- Fold the excess paperback or trim it off.
- That’s all! Your pentagon shape is now ready for admiration! All sides and angles should have the same length and angle.
Pentagon Shape FAQs
How many vertices does a pentagon have?
A pentagon is made up of five straight sides and five vertices (corners). It has five angles inside that total 540°.
What is a house shape called?
A pentagon is a five-sided geometric shape with five angles. “Penta” stands for five, and “gon” stands for angle. A regular pentagon’s interior angles add up to 540 degrees.
What are the types of pentagons?
The following are the various types of pentagons:
- Simple pentagon
- Complex pentagon
- Regular pentagon
- Irregular pentagon
- Concave pentagon
- Convex pentagon
- Equilateral pentagon
- Cyclic pentagon
Hope that with the above information, you can find the best way to help your kids grasp the answer to the question “what is a pentagon?” If you are planning to teach your kids about this essential topic, you can make your own collections of pentagon worksheets using our worksheet generator.
