Have you ever had a moment when you were staring at a shape and realized you had no idea what to call it? Maybe it had five sides and you thought, “hmm, what is a five sided polygon called?” The answer is a pentagon. It’s a shape that is often used in architecture, and even in government buildings like the Pentagon in Washington, D.C.
But why is it important to know this? Well, for starters, it’s always good to expand your knowledge and vocabulary. And if you’re ever playing a trivia game, it might come in handy to know what a pentagon is. Plus, it’s interesting to think about the different shapes and patterns that make up the world around us.
So, the next time you come across a five-sided shape, you’ll be able to impress your friends (or at least yourself) with your newfound knowledge. And who knows, maybe it will spark a curiosity to learn more about geometry and mathematics. The possibilities are endless once you start exploring the world of shapes and numbers.
Types of Polygons
Polygons are two-dimensional shapes formed by straight lines connecting their endpoints. They come in different shapes and sizes, and their unique properties make them fascinating objects to study.
There are different types of polygons classified based on their number of sides and angles. In this article, we will shed some light on the most common types of polygons.
- Triangle: The simplest polygon is a triangle, which has three sides and three angles. It is the only polygon that can exist with fewer than four sides. Depending on its angles, a triangle can be classified into three types: acute, right, or obtuse.
- Quadrilateral: A quadrilateral is a polygon with four sides. It is the most common type of polygon and includes squares, rectangles, parallelograms, trapezoids, and kites. Quadrilaterals can be classified according to their shape and properties.
- Pentagon: A pentagon is a polygon with five sides. It is a unique shape that appears in nature and many man-made structures. A regular pentagon has five equal sides and angles. In contrast, an irregular pentagon has five sides of different lengths and angles.
- Hexagon: A hexagon is a polygon with six sides. It is an efficient shape used in making honeycomb structures, snowflakes, and crystals. A regular hexagon has six equal sides and angles, while an irregular hexagon has six sides of different lengths and angles.
- Octagon: An octagon is a polygon with eight sides. It is a symmetrical and balanced shape used in architecture, art, and design. A regular octagon has eight equal sides and angles, while an irregular octagon has eight sides of different lengths and angles.
Properties of Polygons
Polygons have unique properties that help us identify and classify them. Below are some essential properties of polygons:
- Sides: The number of line segments that form a polygon. Polygons can have three or more sides.
- Vertices: The corners or endpoints of a polygon where two sides meet.
- Angles: The measure of the internal angles formed by the sides of a polygon.
- Area: The amount of surface covered by a polygon measured in square units.
- Perimeter: The total length of the sides of a polygon.
Additionally, polygons can be classified based on their symmetry and tessellation properties. Regular polygons have equal sides and angles and are symmetrical about their center. Tessellations are patterns of polygons that fit together without gaps or overlaps.
Regular Polygons Table
| Polygon | Number of Sides | Interior Angles | Exterior Angles |
|---|---|---|---|
| Triangle | 3 | 60° | 120° |
| Square | 4 | 90° | 90° |
| Pentagon | 5 | 108° | 72° |
| Hexagon | 6 | 120° | 60° |
| Octagon | 8 | 135° | 45° |
The table above shows some examples of regular polygons and their properties. Regular polygons have equal sides and angles, making them easy to work with mathematically and geometrically.
In conclusion, understanding the different types and properties of polygons is crucial in various fields, from mathematics and engineering to art and architecture. Learning about polygons can be both fun and intellectually rewarding.
Geometry Terminologies
One of the most fundamental concepts in geometry is the polygon, a 2-dimensional shape with straight sides and angles. While most polygons have four or more sides, there are some with just five sides. In this article, we will explore what is a five sided polygon called, among other geometry terminologies.
Five Sided Polygon – The Pentagon
- A five sided polygon is called a pentagon.
- The word “pentagon” is derived from the Greek words “penta” meaning “five” and “gonia” meaning “angle”.
- A regular pentagon has all five sides and angles of equal length and measure.
Other Geometry Terminologies
In addition to polygons, there are other important geometry terminologies that are crucial to understanding this subject better. Here are some of them:
- Point: a precise location in space with no dimension.
- Line: a straight path with no thickness or width.
- Angle: the measure of the space between two intersecting lines.
- Triangle: a three-sided polygon.
Types of Triangles
Triangles are classified according to their side lengths and angles. Here are the different types of triangles:
- Equilateral: a triangle with three sides of the same length and three angles of the same measure (60 degrees).
- Isosceles: a triangle with two sides of equal length and two angles of the same measure.
- Scalene: a triangle with no equal sides and no equal angles.
- Right: a triangle with one angle measuring 90 degrees.
Table of Angle Measures of Regular Polygons
Aside from the pentagon, there are many other types of polygons with different numbers of sides, and each has its own unique angle measures. Here is a table of the angle measures of regular polygons (polygons with all sides and angles of the same measure):
| Polygon | Number of Sides | Angle Measures |
|---|---|---|
| Triangle | 3 | 60 degrees each |
| Square | 4 | 90 degrees each |
| Pentagon | 5 | 108 degrees each |
| Hexagon | 6 | 120 degrees each |
| Heptagon | 7 | 128.571 degrees each |
| Octagon | 8 | 135 degrees each |
In conclusion, understanding geometry terminologies is essential in solving problems and equations related to geometry. Knowing the different types of polygons and their unique properties can help you identify and classify geometric shapes more efficiently.
Different shapes in geometry
Geometry is a branch of mathematics focused on the study of shape, size, relative position of objects, and the properties of space. In this article, we will explore the different shapes in geometry, starting with polygons.
Polygons
- A polygon is a two-dimensional closed shape with straight sides.
- It is defined by the number of sides and angles it has.
- Common polygons include triangles, quadrilaterals, pentagons, hexagons, heptagons, octagons, and so on.
Triangles
A triangle is a three-sided polygon. It is the simplest polygon and the building block of other polygons. There are three types of triangles:
- Equilateral triangle: All three sides are of equal length.
- Isosceles triangle: Two sides are of equal length.
- Scalene triangle: All three sides are of different lengths.
Triangles have various properties, such as angles, perimeter, and area, that make them critical in applications that include trigonometry and geometry.
Quadrilaterals
A quadrilateral is a four-sided polygon. There are many types of quadrilaterals, including:
| Type | Description | Properties |
|---|---|---|
| Square | All sides are equal, diagonals are perpendicular bisectors of each other | Equal sides, equal angles, area is s * s (where s is the length of a side) |
| Rectangle | Opposite sides are parallel and equal, diagonals are equal | Opposite sides are equal, four right angles (90 degrees), area is lw (where l is the length and w is the width) |
| Parallelogram | Opposite sides are parallel and equal, opposite angles are equal | Area is bh (where b is the base and h is the height) |
| Trapezoid | One pair of opposite sides are parallel, the other pair is not | Area is ((b1 + b2) * h)/2 (where b1 and b2 are the length of the parallel sides and h is the height from one of the parallel sides to the other) |
Quadrilaterals are used in many fields of work and study, including architecture, engineering, and design.
Conclusion
Geometry is all around us, and understanding the different shapes in geometry is essential in many fields. From triangles to quadrilaterals and beyond, each polygon has unique properties that make it useful in various applications.
Regular polygons
Regular polygons are polygons that have equal side lengths and equal angles between each side. They are named with the prefix “regular” followed by the number of sides the polygon has. For instance, a regular three-sided polygon is called an equilateral triangle, while a regular four-sided polygon is called a square.
- Regular polygons have a fixed perimeter: With regular polygons, all side lengths are equal, thus the perimeter is fixed, eliminating the need to measure each individual side. To find the perimeter of any regular polygon, multiply the number of sides by the length of one side.
- The interior angles of a regular polygon are regular: The interior angles of a regular polygon add up to a constant value. The formula for the interior angle in degrees is (n-2) x 180/n, where n is the number of sides. This is an important property to consider when solving problems involving regular polygons.
- Regular polygons have rotational symmetry: Regular polygons have rotational symmetry. This means that you can rotate a regular polygon by a certain angle and it will look the same as its original position. The angle you need to rotate a regular polygon to make it look the same again is 360/n degrees, where n is the number of sides.
Examples of regular polygons:
Here are some examples of regular polygons with their corresponding number of sides:
| Polygon | Number of Sides |
|---|---|
| Equilateral triangle | 3 |
| Square | 4 |
| Pentagon | 5 |
| Hexagon | 6 |
| Heptagon | 7 |
| Octagon | 8 |
Regular polygons exist with any number of sides, though most have specific names only up to twelve sides. Beyond twelve sides, they are simply called n-gons.
Irregular Polygons
Irregular polygons are those that do not have sides of equal length or angles that have equal measures. There are many different types of irregular polygons, including triangles, quadrilaterals, pentagons, and more. In this article, we will focus on irregular polygons that specifically have five sides.
What is a Five Sided Polygon Called?
- A five-sided polygon is called a pentagon.
- The word “pentagon” comes from the Greek words “pente” meaning “five” and “gonia” meaning “angle”.
- There are many different types of pentagons, including regular and irregular pentagons.
Types of Irregular Pentagons
Irregular pentagons can be classified into different types based on their properties, such as symmetry, angles, and sides. Here are some examples:
- Scalene pentagon: a pentagon with no sides or angles that are equal.
- Acute pentagon: a pentagon in which all interior angles are less than 90 degrees.
- Obtuse pentagon: a pentagon in which one interior angle is greater than 90 degrees.
- Convex pentagon: a pentagon in which all interior angles are less than 180 degrees and all vertices point outward.
- Concave pentagon: a pentagon in which at least one interior angle is greater than 180 degrees and some vertices point inward.
Examples of Irregular Pentagons
Here are some examples of irregular pentagons:
| Pentagon Type | Description | Image |
|---|---|---|
| Scalene | No sides or angles are equal |  |
| Acute | All interior angles are less than 90 degrees |  |
| Obtuse | One interior angle is greater than 90 degrees |  |
| Convex | All interior angles are less than 180 degrees and all vertices point outward |  |
| Concave | At least one interior angle is greater than 180 degrees and some vertices point inward |  |
Irregular polygons, including pentagons, can be found in many real-life objects, such as the shape of leaves, roofs, and more. Understanding their properties and classifications can help us appreciate their beauty and use them in various applications.
Naming Polygons
Naming polygons is a crucial step in geometry as it helps you identify and differentiate between different shapes. Polygons are classified based on the number of sides they have, and it is important to know the names of polygons based on their sides.
Here are some subtopics that can help you understand how polygons are named:
Subsection 6: Naming polygons based on the number of sides
Polygons can have any number of sides, but some polygons have specific names based on the number of sides they have. Here are the most common polygons based on their sides:
- 3 sides – Triangle
- 4 sides – Quadrilateral
- 5 sides – Pentagon
- 6 sides – Hexagon
- 7 sides – Heptagon
- 8 sides – Octagon
- 9 sides – Nonagon
- 10 sides – Decagon
As you can see, polygons are named using Greek prefixes with ‘-gon’ suffix. These prefixes specify the number of sides a polygon has, and the suffix ‘-gon’ means ‘angle.’ For example, a six-sided polygon is called a ‘hexagon’ as ‘hex’ means ‘six’ in Greek.
Here is a table that can help you understand the names of polygons based on the number of sides they have:
| Number of Sides | Name of Polygon |
|---|---|
| 3 | Triangle |
| 4 | Quadrilateral |
| 5 | Pentagon |
| 6 | Hexagon |
| 7 | Heptagon |
| 8 | Octagon |
| 9 | Nonagon |
| 10 | Decagon |
Knowing the names of polygons and their sides can help you in geometry problems and make it easier to communicate with others in mathematical discussions. Additionally, learning the names of polygons can be fascinating and exciting as you delve deeper into the world of geometry.
Properties of polygons
Polygons are two-dimensional shapes with three or more straight sides. Understanding the properties of polygons is important for geometry and measurement. Here are some key properties of polygons:
- Number of sides: Polygons can have three or more sides. For example, a three-sided polygon is called a triangle, while a five-sided polygon is called a pentagon.
- Interior angles: The interior angles of a polygon can be found by using the formula (n-2) x 180, where n is the number of sides. For example, a pentagon has (5-2) x 180 = 540 degrees total interior angle measure, which means if you added all the angles inside a pentagon together, you would get 540 degrees.
- Exterior angles: The exterior angles of a polygon always add up to 360 degrees, regardless of the number of sides.
- Types: Polygons can be classified as regular or irregular. A regular polygon has congruent sides and angles, while an irregular polygon does not.
- Diagonals: A diagonal is a line segment connecting two non-adjacent vertices of a polygon. The number of diagonals in a polygon can be found by using the formula n(n-3)/2, where n is the number of sides.
- Area: The area of a polygon can be found by using various formulas, depending on the shape of the polygon.
- Circumference: The circumference of a polygon can be found by adding the lengths of all the sides.
The 5-Sided Polygon
A five-sided polygon is called a pentagon. It is a regular polygon, meaning it has five congruent sides and five congruent angles. The sum of the interior angles of a pentagon is 540 degrees, and the exterior angles are 72 degrees each. The diagonals of a pentagon can be found using the formula n(n-3)/2, which in this case is 5(5-3)/2 = 5. This means a pentagon has five diagonals.
| Properties of a Regular Pentagon | Measurements |
|---|---|
| Number of sides | 5 |
| Number of angles | 5 |
| Internal angle measure | 108 degrees |
| External angle measure | 72 degrees |
| Diagonals | 5 |
| Area | [(1/4) × sqrt(5 × (5 + 2 × sqrt(5))) × a²], where a is the length of a side |
| Circumference | 5a, where a is the length of a side |
Understanding the properties of polygons, such as the five-sided polygon or pentagon, can help in identifying and solving geometric problems in various areas of study such as architecture, engineering, and design.
What is a Five Sided Polygon called FAQ
1. What is a five-sided polygon called?
A five-sided polygon is called a pentagon.
2. How do you know if a shape is a pentagon?
If a shape has five sides and all the sides are straight and of equal length, then it is a pentagon.
3. What are the properties of a pentagon?
A pentagon has five sides and five angles. The sum of the interior angles of a pentagon is 540 degrees.
4. Can a pentagon be regular?
Yes, a pentagon can be regular, which means all of its sides and angles are of equal measure.
5. What are some examples of pentagons in nature?
Many flowers, such as the morning glory and the sweet pea, have pentagon-shaped petals. The shape of a starfish is also pentagon-like.
6. What is the difference between a pentagon and a hexagon?
A pentagon has five sides, while a hexagon has six sides.
7. How are pentagons used in architecture?
Pentagons can be used in the design of buildings, such as the Pentagon in Washington D.C., which is shaped like a pentagon, or in the design of windows or building facades.
Closing Thoughts
Thanks for reading about pentagons today. We hope you learned a lot about this interesting shape and its properties. Make sure to visit again later for more interesting information about geometry and other topics that pique your interest!