A Polygon With 7 Sides Is Called What?
Geometry can be a fascinating subject to learn. It is the branch of mathematics that deals with shapes, sizes, positions, and dimensions of objects. One of the fundamental concepts of geometry is the polygon. A polygon is a two-dimensional shape that is made up of straight lines and angles. It is a closed figure with three or more sides. In this article, we will be discussing a polygon with seven sides and what it is called.
Definition of a Polygon
Before we dive into what a polygon with seven sides is called, let us first define what a polygon is. A polygon is a flat, closed shape that has three or more straight sides and angles. The sides of a polygon do not cross each other, and the angles between adjacent sides are always the same. Polygons are classified based on the number of sides they have, and each polygon has a unique name.
What is a Polygon with 7 Sides Called?
A polygon with seven sides is called a heptagon. The word heptagon is derived from the Greek words "hepta" which means seven and "gonia" which means angles. Therefore, a heptagon is a seven-sided polygon with seven angles.
Properties of a Heptagon
A heptagon has several properties that make it unique. First, all the interior angles of a heptagon add up to 900 degrees. Each angle of a regular heptagon measures 128.57 degrees. Second, a heptagon has seven diagonals, which are line segments that connect two non-adjacent vertices. A regular heptagon has 14 diagonals, while an irregular heptagon has more than 14 diagonals.
Examples of Heptagons in Real Life
Heptagons can be found in many real-life objects and structures. One example is the seven-sided stop sign that is commonly used in traffic control. Another example is the shape of some coins, such as the 50 pence coin in the United Kingdom. The Seven Sisters Cliffs in England are also named after the heptagon shape.
How to Calculate the Area of a Heptagon
To calculate the area of a heptagon, you need to know the length of its sides and the apothem, which is the distance from the center of the heptagon to the midpoint of any side. The formula for calculating the area of a regular heptagon is:
Area = (7/4) x a2 x cot(π/7)
Where a is the length of each side of the heptagon.
Challenges Involving Heptagons
Heptagons can be used in several challenging problems in geometry. One example is constructing a heptagon using only a compass and a straightedge. This problem has been studied by mathematicians for centuries, and it was only in 1832 when it was finally proved that it is impossible to construct a regular heptagon using only a compass and a straightedge.
Other Polygons with Seven Sides
Aside from the heptagon, there are other polygons that have seven sides. These include the heptagram, which is a seven-pointed star with seven sides, and the irregular heptagon, which is a heptagon with sides and angles of different lengths and measures.
Conclusion
Geometry is a fascinating subject that deals with the study of shapes, sizes, positions, and dimensions of objects. In this article, we discussed the concept of polygons and their properties. We also learned that a polygon with seven sides is called a heptagon and that it has several unique properties. Heptagons can be found in many real-life objects and structures, and they can be used in several challenging problems in geometry.
In conclusion, a polygon with 7 sides is called a heptagon, and it is a fascinating shape to study in geometry.
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