Are you someone who struggled in geometry class, particularly when it came to identifying shapes? Maybe you’re like me, and you’ve encountered a polygon with four straight sides and you’re not quite sure what to call it. Well, fear not my friend, because in this article I’m going to answer the question that’s been bugging you: what is a four sided shape called?
Before we dive into the specifics of the four sided shape, let’s take a moment to appreciate the role that geometry plays in our everyday lives. From designing buildings to cracking codes, geometry is the foundation of everything that is visually appealing or mathematically complex. It’s no wonder that geometry is a core subject in our education system and is essential for problem-solving and logical reasoning. And speaking of problem-solving, that’s precisely what we’re doing today! We’re here to solve the age-old question of what a four sided shape is called.
So, let’s get started! The four sided shape that has been plaguing you is called a quadrilateral. That’s right, the lesser-known cousin of the triangle and the circle. The word quadrilateral is derived from the Latin words “quattuor” meaning “four,” and “latus” meaning “side.” A quadrilateral is a geometric figure with four straight sides and four angles, opposite angles are equal, and the total of all the angles is 360 degrees. Now that you know what it’s called let’s delve a little deeper into the different types of quadrilaterals and their properties.
Types of Geometric Shapes
Geometric shapes are figures that are formed by connecting different points in space. These shapes are classified based on the number of sides or edges they have. The most common shapes are two-dimensional, having only height and width, but some have a third dimension, which is depth. These shapes are often used in geometry, mathematics, construction, engineering, and art.
The Four-sided Shape: Quadrilaterals
A quadrilateral is a term used to describe any four-sided shape. It is made up of four straight sides and four angles which add up to 360 degrees. These shapes are found almost everywhere in the world, from buildings to everyday objects. The word quadrilateral comes from Latin, meaning “four sides.”
Quadrilaterals can be divided into different types based on their properties:
- Rectangle: a quadrilateral with four right angles and two pairs of matching sides
- Square: a rectangle with four equal sides
- Parallelogram: a quadrilateral with opposite sides parallel to each other
- Trapezoid: a quadrilateral with at least one pair of parallel sides
- Rhombus: a quadrilateral with four equal sides but not all angles are right angles
Each of these types of quadrilaterals has unique properties that make them different from the others. For example, a square is a type of rectangle with the same length on all four sides, while a parallelogram has opposite sides that are parallel to each other but may not be equal in length or perpendicular.
| Type of Quadrilateral | Properties |
|---|---|
| Rectangle | Four right angles, two pairs of matching sides |
| Square | Four equal sides, four right angles |
| Parallelogram | Opposite sides parallel to each other, opposite sides equal in length |
| Trapezoid | At least one pair of parallel sides |
| Rhombus | Four equal sides, opposite angles equal in measure, diagonals perpendicular to each other |
The study of geometry involves understanding the properties and relationships of different shapes. Knowing the different types of quadrilaterals and how they are used can help in solving problems involving these shapes.
Characteristics of Quadrilaterals
Quadrilaterals are four-sided shapes that are composed of straight lines and angles. They are classified according to their sides and angles, and each type of quadrilateral has its unique characteristics.
The Types of Quadrilaterals
- Square: A quadrilateral with four equal sides and four right angles. All squares are rectangles and all rectangles are parallelograms.
- Rectangle: A quadrilateral with four right angles. Opposite sides are parallel and of equal length.
- Parallelogram: A quadrilateral with opposite sides parallel. Opposite angles are equal.
Properties of Quadrilaterals
All quadrilaterals have certain properties that are true for all of them:
- Interior Angles: The sum of the interior angles of a quadrilateral is always 360 degrees.
- Opposite Angles: Opposite angles of a quadrilateral are equal.
- Consecutive Angles: Consecutive angles of a quadrilateral always add up to 180 degrees.
Special Properties of Quadrilaterals
Each type of quadrilateral has special properties that are unique:
| Type | Definition | Special Properties |
|---|---|---|
| Square | A quadrilateral with four equal sides and four right angles. | All squares are rectangles and have two diagonals that are equal in length and bisect each other. |
| Rectangle | A quadrilateral with four right angles. | Opposite sides are parallel and of equal length. Two diagonals are equal in length and bisect each other. |
| Parallelogram | A quadrilateral with opposite sides parallel. | Opposite sides are equal in length. Opposite angles are equal. Diagonals bisect each other. |
Understanding the characteristics and properties of quadrilaterals is crucial in solving geometric problems, especially in trigonometry and geometry.
Naming Four-Sided Shapes
Four-sided shapes, also known as quadrilaterals, are a fundamental concept in geometry that many of us come across as early as elementary school. These shapes can vary in size, angles, and side lengths, but they all share one common characteristic – they have four sides. Understanding the names of these shapes is crucial when it comes to practical applications such as construction, architecture, and even graphic design.
The Three Subcategories of Quadrilaterals
- Trapezoids: A trapezoid is a quadrilateral with only one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs.
- Parallelograms: A parallelogram is a quadrilateral with opposite sides that are parallel. The opposite sides are also the same length, and the opposite angles are congruent.
- Special Quadrilaterals: This category includes shapes such as rectangles, squares, and rhombuses. They have unique properties that set them apart from other quadrilaterals.
Understanding the differences between these three categories is important when it comes to solving mathematical problems or design work. In certain scenarios, specific types of quadrilaterals might be required, and understanding the subcategories will narrow down the pool of options to choose from, resulting in a more accurate solution.
It’s worth noting that sometimes a quadrilateral might fall into more than one category, such as a rectangle also being a parallelogram. In these cases, the shape is referred to using the name of the most specific category it falls under. For example, a rectangle would be referred to as a rectangle, not a parallelogram.
Becoming familiar with the different types of quadrilaterals is a fundamental step towards a solid foundation in geometry. The table below summarizes the characteristics of each subcategory of quadrilaterals.
| Type of Quadrilateral | Number of Pairs of Parallel Sides | Opposite Sides Congruent? | Opposite Angles Congruent? |
|---|---|---|---|
| Trapezoid | 1 | No | No |
| Parallelogram | 2 | Yes | Yes |
| Rectangle | 2 | Yes | Yes |
| Rhombus | 2 | Yes | No |
| Square | 2 | Yes | Yes |
By understanding the differences between each type of quadrilateral and their unique properties, you’ll have a solid foundation to build upon when it comes to more advanced geometric concepts.
Properties of Parallelograms
Parallelograms are four-sided figures with two pairs of parallel sides. They have many unique properties that distinguish them from other shapes. Understanding these properties can help us better understand the geometry of parallelograms.
The Number 4
The number 4 is crucial to the definition of a parallelogram. A parallelogram is defined as a four-sided figure with two pairs of parallel sides. This property makes it possible for parallelograms to have a variety of other properties that are unique to them.
- Opposite Sides are Congruent: In a parallelogram, the two pairs of opposite sides are congruent. This means that if we measure the length of one side of the parallelogram, we can use that measurement to find the length of the opposite side.
- Opposite Angles are Congruent: Another unique property of parallelograms is that opposite angles are congruent. This means that if we measure the measure of one angle, we can use that measurement to find the measure of the opposite angle.
- Consecutive Angles are Supplementary: Consecutive angles in a parallelogram are supplementary. This means that the sum of any two consecutive angles is 180 degrees.
Other Properties of Parallelograms
In addition to the properties mentioned above, parallelograms have a number of other interesting properties that make them unique.
Diagonals: The diagonals of a parallelogram bisect each other. This means that the point where the diagonals intersect is the midpoint of both diagonals.
Area: The area of a parallelogram can be found by multiplying the base by the height. The base is any of the parallel sides, and the height is the distance between the two parallel sides.
Perimeter: The perimeter of a parallelogram is found by adding the lengths of all four sides.
| Property | Formula |
|---|---|
| Area | base x height |
| Perimeter | sum of all sides |
Understanding the properties of parallelograms is important for various applications, such as in engineering and architecture. Knowing these properties can help us to accurately measure and construct parallelograms, making them an essential part of geometry.
Differentiating Rhombuses from Squares
It is common for people to mistake a rhombus for a square and vice versa. Although both shapes have four sides with congruent sides and opposite angles that are equal, there are distinct differences between the two shapes. Here, we’ll dive deeper into these differences.
- Angles: A square has four right angles, meaning each angle measures 90 degrees. On the other hand, a rhombus has two opposite angles measuring acute (less than 90 degrees) and two opposite angles measuring obtuse (greater than 90 degrees).
- Parallel sides: A square has parallel sides opposite to each other, while a rhombus does not have parallel sides.
- Diagonals: A square has two diagonals that are equal in length, are bisecting each other, and creates four congruent right triangles. In contrast, the diagonals of a rhombus do not bisect each other and are not perpendicular to one another.
Here’s a quick way to differentiate a square from a rhombus: if all angles are equal and perpendicular, it is most definitely a square. But, if the sides are all congruent, but the opposite side angles are not perpendicular, then it’s probably a rhombus.
Knowing the distinctions between a rhombus and a square can come in handy, especially when solving geometry problems or attempting to identify different shapes in real life. Mastering these differences can also help you stand out in math class and impress your teacher. So, next time you come across either of these four-sided figures, you’ll know how to tell them apart with ease.
| Number of congruent sides | Measure of angles | Opposite angles | Parallel sides | Diagonals | |
|---|---|---|---|---|---|
| Square | 4 | 90° | Equal and Perpendicular | Opposite and Parallel | Equal and Bisecting |
| Rhombus | 4 | Equal | Equal and Not Perpendicular | No Opposite Sides Parallel | Unequal and Not Bisecting |
There you have it! If you’re ever unsure whether you’re looking at a rhombus or square, keep these differences in mind.
Trapezoids vs. Kites
When we hear the term “four-sided shape,” the first thing that comes to mind is probably a square or a rectangle. However, there are two other important types of quadrilaterals that we should know about – the trapezoid and the kite.
- Trapezoid: A trapezoid is a quadrilateral with one pair of parallel sides. The other two sides can be equal or unequal in length. The parallel sides are called the bases, and the non-parallel sides are called the legs.
- Kite: A kite is a quadrilateral with two pairs of adjacent sides that are equal in length. The diagonals of a kite are perpendicular to each other, and one of the diagonals bisects the other.
- Differences: The main difference between trapezoids and kites is that trapezoids have one pair of parallel sides, while kites have two pairs of equal-length adjacent sides. Additionally, the legs of a trapezoid can be of different lengths, while the sides of a kite are always equal in length. Another distinguishing feature is that the two diagonals of a trapezoid are not equal in length, while the two diagonals of a kite are equal in length.
Trapezoids and Kites in Real Life
Trapezoids and kites are important shapes in many areas of life, including architecture, engineering, and art. In architecture and engineering, trapezoids are often used in the design of roofs, while kites are used in the design of bridges and other structures. In art, both trapezoids and kites are popular shapes for creating dynamic compositions, as their asymmetrical sides can create visual movement and tension.
Trapezoids vs. Kites: Area and Perimeter
Calculating the area and perimeter of trapezoids and kites involves different formulas, due to their unique properties. The area of a trapezoid can be found with the formula:
Area = ((b1 + b2) / 2) x h
Where b1 and b2 are the lengths of the two bases, and h is the height (the perpendicular distance between the two bases).
The perimeter of a trapezoid can be found by simply adding up the lengths of all four sides.
Kites, on the other hand, have two different formulas for area and perimeter, depending on what information is given. If the lengths of both diagonals are known, the area can be found with the formula:
Area = (d1 x d2) / 2
Where d1 and d2 are the lengths of the diagonals.
If the lengths of the sides are known, the area can be found with Heron’s Formula:
Area = √s(s-a)(s-b)(s-c)
Where s is the semiperimeter (half the perimeter) and a, b, and c are the lengths of the sides.
The perimeter of a kite can be found by simply adding up the lengths of all four sides.
| Property | Trapezoid | Kite |
|---|---|---|
| No. of parallel sides | 1 | 0 |
| No. of pairs of adjacent sides of equal length | 0 | 2 |
| Diagonals | Unequal in length | Perpendicular; one bisects the other |
Now that we understand the differences between trapezoids and kites, and how to calculate their area and perimeter, we can appreciate the unique properties of these important quadrilaterals.
Applications of Four-Sided Shapes in Real Life
Four-sided shapes, also known as quadrilaterals, are ubiquitous in everyday life. From the buildings we live and work in to the objects we use on a daily basis, these shapes surround us constantly. Here are just a few of the many applications of four-sided shapes in real life.
The Seven Types of Quadrilaterals
- The first type of quadrilateral is the square. This shape has four congruent sides and four right angles.
- The second type is the rectangle. Like the square, it has four right angles, but its sides are not congruent.
- The third type is the parallelogram. This shape has two pairs of parallel sides.
- The fourth type is the rhombus. Like the parallelogram, it has two pairs of parallel sides, but its sides are all congruent.
- The fifth type is the trapezoid. This shape has one pair of parallel sides.
- The sixth type is the kite. This shape has two pairs of adjacent sides that are congruent.
- The seventh and final type is the irregular quadrilateral. This catch-all category includes any quadrilateral that does not fit into the other six categories.
Understanding the characteristics of these seven types of quadrilaterals can help in a variety of real-life situations.
Building and Construction
In building and construction, quadrilaterals are used extensively. When designing a building, architects and engineers must take into account the properties of different quadrilaterals in order to determine which shapes will provide the necessary support and stability. For example, squares and rectangles are often used as building blocks for foundations and walls, as their right angles and congruent sides make them ideal for bearing weight and maintaining structural integrity.
Eyeglasses
Many eyeglasses are designed with quadrilateral shapes, such as rectangles and trapezoids, in order to provide the best fit for the wearer. By using these shapes, designers are able to create frames that contour to the shape of the head and face, providing a secure and comfortable fit without slipping or sliding. This is especially important for those who require prescription lenses and who wear their glasses on a daily basis.
Art and Design
Quadrilaterals are also used extensively in art and design. In graphic design, quadrilaterals are often used to create shapes and images, and in photography, the use of quadrilaterals—such as rectangles and squares—can help to frame and focus the image. Additionally, many artists use quadrilaterals to create geometric designs and patterns, which can be found in everything from textiles and ceramics to jewelry and home decor.
Conclusion
| Quadrilateral Type | Characteristics | Real-Life Applications |
|---|---|---|
| Square | Four congruent sides, four right angles | Foundations, walls |
| Rectangle | Four right angles, sides not congruent | Eyeglasses, shelves, doors |
| Parallelogram | Two pairs of parallel sides | Roof trusses, girders, bridges |
| Rhombus | Two pairs of parallel sides, all sides congruent | Tile patterns, quilt patterns |
| Trapezoid | One pair of parallel sides | Picture frames, tent flys, roof design |
| Kite | Two pairs of adjacent sides that are congruent | Sail design, paper airplanes |
| Irregular Quadrilateral | No set characteristics | Catch-all category for shapes that do not fit into other six categories |
Now that you know more about the different types and real-life applications of four-sided shapes, you may start seeing them everywhere you go. From the buildings you live in to the patterns on your clothes, these shapes play a significant role in our surroundings and can lend themselves to a myriad of uses and designs.
What is a Four Sided Shape Called FAQs
Q. What is a four sided shape called?
A. A four-sided shape is called a quadrilateral.
Q. What are some examples of quadrilaterals?
A. Some examples of quadrilaterals are squares, rectangles, trapezoids, kites, and parallelograms.
Q. How are quadrilaterals different from triangles?
A. Quadrilaterals have four sides and four angles, while triangles have three sides and three angles.
Q. Can a quadrilateral have two sides of different lengths?
A. Yes, a quadrilateral can have two sides of different lengths, such as a trapezoid.
Q. Is a square a type of rectangle?
A. Yes, a square is a type of rectangle with four equal sides.
Q. How many degrees are in the angles of a quadrilateral?
A. The angles in a quadrilateral always add up to 360 degrees.
Q. Are all parallelograms also rectangles?
A. No, not all parallelograms are rectangles. A rectangle has four right angles, while a parallelogram has two pairs of parallel sides.
Closing Thoughts
Thanks for reading about what a four sided shape is called! Quadrilaterals are a fascinating part of geometry, with a wide range of shapes and sizes. Whether you’re working on homework or just want to learn more about math, remember to visit us again for more interesting articles!