Learning Materials
Features
Discover
Have you ever looked at a chess or checkers board and thought to yourself, "Wow, this is a fine-looking perfect square!"? Without realizing it, this square chess board is considered a special quadrilateral. In this article, we will discuss:
Millions of flashcards designed to help you ace your studies
Sign up for free
Achieve better grades quicker with Premium
Geld-zurück-Garantie, wenn du durch die Prüfung fällst
Did you know that StudySmarter supports you beyond learning?
Review generated flashcards
Start learning or create your own AI flashcards
Team Special quadrilaterals Teachers
Five types of special quadrilaterals (kites, rhombuses, rectangles, squares, and trapezoids)
Some properties of each
For more information on each type of these special quadrilaterals, check out our articles on Rectangles, Squares, Rhombuses, and Trapezoids.
First, let's review quadrilaterals. You can find more details in Quadrilaterals.
Let's recall what we mean when we say "quadrilateral". For more details, see our article on Quadrilaterals.
A quadrilateral is a two-dimensional figure. It is a type of polygon, and what makes a figure a quadrilateral is the fact that it has four sides.
"Quadri" in the word "quadrilateral" is a Latin word that means 4. The word "lateral" means "sides. That is why a figure with four sides is called a quadrilateral.
Some quadrilaterals don't have any matching side lengths or angles, like in the figure below.
A shape with no equal sides or angles - Vaia Originals
Some have pairs of congruent side lengths and angles, like in the figure below:
A diagram of a rectangle - Vaia Originals
This article will focus on the latter of these two examples (quadrilaterals that have some combination of equal side lengths and/or angles). Let's have a further look!
Special quadrilaterals are polygons with four sides that have some combination of equal side lengths and/or angles.
A polygon is a two-dimensional, enclosed figure (such as a triangle or square). Refer to the article on Polygons for specifics!
The five types of special quadrilaterals are:
Rhombus
Square
Trapezoid
Kites
Let's take a look at the properties of each quadrilateral.
Now, let's look at what makes the special quadrilaterals so special. They each have their unique properties, but you will find that some of them have some similarities. Let's start with a rectangle.
A rectangle is a quadrilateral with opposite parallel sides of equal length and four equal right angles of 90 degrees each. The figure below shows a rectangle.
A diagram of a rectangle - Vaia OriginalsThe opposite sides of a rectangle are equal and parallel to each other.
It has four equal angles of 90 degrees.
The diagonals bisect each other.
The sum of the angles in a rectangle is 360 degrees.
Remember that to bisect means to divide into parts.
A square is a quadrilateral with opposite sides parallel to each other. They also have four equal angles and sides. Just like the rectangle, the angles are 90 degrees each. The figure below is a square.
A diagram of a square - Vaia Originals
All sides of a square are equal.
The opposite sides are parallel.
The diagonals bisect each angle.
It has four equal angles of 90 degrees.
The length of the diagonals is longer than the sides of the square.
The sum of the angles in a square is 360 degrees.
The rhombus is a quadrilateral with equal sides. The opposite sides are parallel to each other. A rhombus also has equal opposite angles.
A diagram of a rhombus - Vaia Originals
The opposite sides of a rhombus are equal and parallel.
The opposite angles of a rhombus are equal.
The diagonals bisect each other.
The diagonals of a rhombus bisect each angle.
A rhombus, square, and rectangle are known as parallelograms. You can find out more about them from our article on the Properties of parallelograms.
A trapezoid is a quadrilateral. However, it is not a parallelogram because it has just one pair of parallel sides. The parallel sides are called the bases, and the other two sides are called the legs. The angles in a trapezoid are called base angles.
A diagram of a trapezoid - Vaia OriginalsJust one pair of the opposite sides (the base) are parallel.
The sum of any 2 angles next to each other is 180 degrees.
There are a few types of trapezoids that give themselves additional unique properties. You can read more about these in the article on Trapezoids.
The kite is our final type of special quadrilateral. It has two pairs of congruent sides that are adjacent to each other. The figure below shows a kite.
A diagram of a kite - Vaia Originals
You may need to find the area or the perimeter of the quadrilaterals. The formula used to get these depends on the quadrilateral in question. You can find more details in the Area of plane figures folder. Let's see the various formulas used to get the area and perimeter of special quadrilaterals.
The area of a rectangle is the product of its length (L) and breadth (B). A rectangle has equal opposite sides. So, when finding the area, you need to use the value of one of its opposite sides. You can determine the perimeter by adding all the sides together. Let's look at the formulas:
A diagram of a rectangle - Vaia Originals
A square has four equal sides. Let's look at the area and perimeter of a square.
A diagram of a square - Vaia Originals
The area of a rhombus is half the product of the length of its diagonals. The perimeter of a rhombus is the summation of all its equal sides or 4 times the side length.
A diagram of a rhombus - Vaia Originals
The area of a trapezoid is half the product of the sum of the parallel sides and the height. The perimeter of a trapezoid is the sum of all the sides.
A diagram of a trapezoid - Vaia Originals
The area is a kite if half the product of the diagonals.
A diagram of a kite, Vaia Originals
In the diagram above, the area is
Sign up for free to gain access to all our flashcards.
What are special quadrilaterals?
Special quadrilaterals are quadrilaterals with some or all equal sides and angles.
What makes a quadrilateral?
A quadrilateral is made up of four sides and four angles.
What are the properties of special quadrilaterals?
The properties of special quadrilaterals depends on the type of quadrilateral that is being examined.
What are examples of special quadrilaterals?
Examples of special quadrilaterals are square, rectangle, rhombus and trapezoid.
What is the formula used for special quadrilaterals?
The formula used for special quadrilaterals depends on the type of quadrilateral in questions. There are different formulas used to calculate the area and perimeter of different special quadrilaterals.
At StudySmarter, we have created a learning platform that serves millions of students. Meet the people who work hard to deliver fact based content as well as making sure it is verified.
Lily Hulatt is a Digital Content Specialist with over three years of experience in content strategy and curriculum design. She gained her PhD in English Literature from Durham University in 2022, taught in Durham University’s English Studies Department, and has contributed to a number of publications. Lily specialises in English Literature, English Language, History, and Philosophy.
Get to know Lily
Gabriel Freitas is an AI Engineer with a solid experience in software development, machine learning algorithms, and generative AI, including large language models’ (LLMs) applications. Graduated in Electrical Engineering at the University of São Paulo, he is currently pursuing an MSc in Computer Engineering at the University of Campinas, specializing in machine learning topics. Gabriel has a strong background in software engineering and has worked on projects involving computer vision, embedded AI, and LLM applications.
Get to know Gabriel
Vaia is a globally recognized educational technology company, offering a holistic learning platform designed for students of all ages and educational levels. Our platform provides learning support for a wide range of subjects, including STEM, Social Sciences, and Languages and also helps students to successfully master various tests and exams worldwide, such as GCSE, A Level, SAT, ACT, Abitur, and more. We offer an extensive library of learning materials, including interactive flashcards, comprehensive textbook solutions, and detailed explanations. The cutting-edge technology and tools we provide help students create their own learning materials. StudySmarter’s content is not only expert-verified but also regularly updated to ensure accuracy and relevance.
Learn moreSave explanations to your personalised space and access them anytime, anywhere!
Sign up with Email Sign up with AppleBy signing up, you agree to the Terms and Conditions and the Privacy Policy of Vaia.
Already have an account? Log in
Sign up to highlight and take notes. It’s 100% free.
Explanations 
Textbooks 
Exams 
GCSE 
IGCSE 
AS 
A Level 
International A Level 
University Admissions Tests 
Flashcards 
Vaia AI 
Notes 
Study Plans 
Study Sets 
Find a job 
Find a degree 
Student Deals 
Magazine 
Mobile App 
