What is a 7-sided shape called? A heptagon is a kind of shape that exists only in two dimensions and contains seven edges, seven vertices, and seven angles. In certain circles, it is also referred to as a septagon or a 7-gon. In a hexagon, you’ll find a total of fourteen diagonals. In this article, we will look at the heptagon and discuss its shape as well as its properties.
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What is a Heptagon?
A heptagon is a kind of form that is only two-dimensional and has seven sides as well as seven angles. It belongs to the class of polygons that are defined by geometry in two dimensions. Polygons are closed geometric structures that only have straight edges and no curved edges.
In Greek, “hepta” refers to the number seven, while “gonia” is the word for an angle. The combination of these two words results in the formation of the word “heptagon,” which refers to a shape with seven different angles. In Latin, this particular polygon is known as a septagon, where “septa” refers to the number seven and “gon” refers to the angle.
Both regular and irregular variations of heptagons are available. A heptagon is said to be regular if it has sides and angles that are congruent to one another and if all of its sides, including the interior angles, are equal.
Based on the characteristics, heptagons may also be characterized as either concave or convex shapes. The term “convex heptagon” refers to a polygon with seven sides and a heptagon shape that incorporates all of the polygon’s diagonals. On the other hand, the sides and angles of a heptagon might be fragmented and irregular if it is considered to be an irregular heptagon.
Heptagonal Definition
Heptagon Sides
A heptagon has seven straight edges, all of which may be the same length or may each have a different length. These two sides meet one another, but they do not cross or intersect with one another. When the sides of the heptagon come together at its vertices, a closed shape with seven sides is produced.
Heptagon Angles
The sum of the heptagon’s seven interior angles, which adds up to 900 degrees, is the heptagon’s total interior angle. A figure can have both acute and obtuse angles. The sum of a heptagon’s outside angles always adds up to 360 degrees, and this is the case whether the heptagon in question is regular or irregular.
Heptagon Diagonals
In a hexagon, you’ll find a total of fourteen diagonals. In a convex heptagon, the diagonals are contained inside the form, but in a concave heptagon, the diagonals extend at least partly outside the boundaries of the heptagon.
Types of Heptagon Shape
There are subtypes of heptagon forms that may be determined by the angles and sides of the shape.
Heptagons may be categorized according to their side lengths
- Regular Heptagon: Equivalent sides and angles define a regular heptagon. The total internal angle of a polygon is equal to (n-2) times 180 degrees, where n is the number of sides of the polygon. Since a heptagon has seven sides, the sum of its interior angles is (7-2) 180 degrees, which is 5 180 degrees, which equals 900 degrees. The internal angle value of a normal heptagon is 900 degrees/7, which equals 128.57 degrees.
- Irregular Heptagon: An example of an irregular heptagon is one in which the side lengths and angle lengths are not all the same size. A value that is exclusive to itself will be assigned to each internal angle that constitutes an irregular heptagon. On the other hand, the sum of the internal angles of an irregular heptagon is also 900 degrees.
Heptagons may be categorized based on angle measurements
- Convex Heptagon: A convex heptagon is characterized by having interior angles that are all less than 180 degrees. There is a possibility that they are regular or irregular heptagons. The vertices of the convex heptagon are all angled outwards toward the outside of the shape.
- Concave Heptagon: A concave heptagon is characterized by the presence of at least one internal angle that is more than 180 degrees. There is a possibility that they are regular or irregular heptagons. At least one of the six vertices of a concave hexagon is angled inward.
Read more >> What Is A 12-Sided Shape?
Properties of Heptagon
Now that we are aware of the fundamental definition of a heptagon, let’s examine some of its key properties.
- There are 7 vertices, 7 edges, and 7 sides in a heptagon.
- A heptagon’s interior angles add up to 900 degrees.
- A regular heptagon’s interior angles have values of 128.57° each.
- A heptagon’s external angles add up to 360 degrees.
- A heptagon may have a maximum of fourteen diagonals.
- A typical heptagon’s central angle has a measurement of around 51.43 degrees.
- Since all of a normal heptagon’s interior angles are smaller than 180 degrees, it is often referred to as a convex heptagon.
- An irregular heptagon has sides that aren’t equal and angles that aren’t the same size.
Regular Heptagon Formula
There are a lot of equations that may be used to describe a regular heptagon. In this lesson, we will learn how to use the formulae for heptagons to calculate the area and perimeter of a standard heptagon.
The perimeter of a Heptagon
We are aware that a typical heptagon has seven sides that are all the same length. As a result, the formula for calculating the perimeter of a normal heptagon is 7 times the side length. In light of this, the formula for calculating the perimeter of a regular heptagon with sides of length is as follows:
Perimeter = 7a
Area of a Heptagon
The whole space that is filled by a heptagon is what is meant to be understood as the heptagon’s area. The formula Area = (7a²/4) cot (π/7) when applied to a regular heptagon with side length a, may be used to get the area of the shape. This formula may be simplified and approximated by writing it as 3.634a2, where ‘a’ refers to the side length. The area of a normal heptagon may be determined by using this information.
Heptagon Angles
A heptagon has seven angles on its internal face and seven angles on its outside face. Let’s become educated on the heptagon’s inside angles as well as its external angles.
Interior Angles of a Regular Heptagon
The interior angle formula for a regular polygon is written as (n-2)×180 degrees, where n is the number of sides of the polygon. This formula is used to get the sum of the internal angles of the polygon. Therefore, the number n for a heptagon is 7. The sum of the inner angles of a regular heptagon is equal to seven and a half degrees times one hundred eighty degrees. Therefore, the measure of each internal angle of a regular heptagon is 900/7, which is equal to 128.57 degrees.
Exterior Angles of a Regular Heptagon
The formula for the summation of exterior angles states that the total amount of a regular polygon’s outside angles must equal 360 degrees for the shape to be considered regular. Therefore, the total exterior angles of a normal heptagon add up to 360 degrees when added together. Therefore, the value of each exterior angle of a regular heptagon is 360/7, which is equal to 51.43 degrees.
Examples of Heptagon
Carriers of Paper
If you follow the outline of a paper boat from edge to edge, you will easily be able to discover all seven of its sides, as well as its seven edges and seven angles. The lengths of the sides and the magnitudes of the angles do not correspond to one another in any way at all. Therefore, a paper boat is an excellent illustration of an irregular heptagon.
Arrowhead
If you take a piece of paper and draw an arrowhead on it, it will have seven sides that are not equal and seven angles that are not equal. Because of this, an arrowhead is an additional illustration of an irregular heptagon. Looking at road signs that are in the form of arrowheads is a good way to get a mental picture of the heptagon, which is a geometric figure.
Pants
One may readily picture the geometric figure of a heptagon when tracing the shape of a pair of jeans because the heptagon consists of seven sides that are uneven in length and seven angles that are unequal in size. This makes the heptagon easy to visualize. As a result, it is the epitome of what is known as an irregular heptagon.
What is a 7-sided shape called? The answer is a heptagon. So now let’s begin to discover the property, formulas, and other examples of heptagon to assist your math-solving process. If you are planning to teach your kids about this essential topic, you can make your own collections of heptagon worksheets using our worksheet maker.
