What Is a Quadrilateral? Definition, Types and Examples
Part of the Math Concepts guide for Grades 3 to 8.
What Is a Quadrilateral?
A quadrilateral is a polygon with exactly four sides, four vertices (corners), and four interior angles. The sum of all interior angles in any quadrilateral is always 360 degrees. The word quadrilateral comes from the Latin words quadri (four) and latus (side). Examples include squares, rectangles, rhombuses, parallelograms, trapezoids, and kites.
The 6 Types of Quadrilaterals
| Type | Defining properties | Real-world example |
|---|---|---|
| Square | 4 equal sides, 4 right angles | Chessboard square |
| Rectangle | Opposite sides equal, 4 right angles | Sheet of paper |
| Rhombus | 4 equal sides, opposite angles equal | Diamond shape on a playing card |
| Parallelogram | Opposite sides parallel and equal | Slanted rectangular shape |
| Trapezoid | Exactly one pair of parallel sides | Cross-section of a bathtub |
| Kite | Two pairs of adjacent equal sides | Traditional flying kite |
Each Type Explained
Square
A square has all four sides equal in length and all four angles equal to 90 degrees. Because of this, a square is also a rectangle and a rhombus at the same time. If you know the side length s, the area = s² and the perimeter = 4s.
Rectangle
A rectangle has opposite sides that are equal and parallel, and all four angles are 90 degrees. Unlike a square, the four sides do not all have to be equal; opposite sides just need to match. Area = length x width, perimeter = 2(l + w).
Rhombus
A rhombus has all four sides equal, but unlike a square, the angles do not need to be 90 degrees. Opposite sides are parallel, and opposite angles are equal. The diagonals bisect each other at right angles. Area = base x height.
Parallelogram
A parallelogram has two pairs of opposite parallel sides, with those opposite sides being equal. Opposite angles are equal, and consecutive angles add up to 180 degrees. Rectangles and rhombuses are special types of parallelograms. Area = base x height.
Trapezoid
A trapezoid has exactly one pair of parallel sides, called the bases. The two non-parallel sides are called the legs. A special case is the isosceles trapezoid, which has equal legs. Area = (1/2)(b₁ + b₂) x h.
Kite
A kite has two pairs of adjacent (touching) sides that are equal. One pair of opposite angles is equal. The diagonals are perpendicular to each other, and one diagonal bisects the other. Area = (d₁ x d₂) ÷ 2.
The Quadrilateral Hierarchy
This is one of those topics where students get confused about which shapes belong inside which categories. Here is a simple way to explain it to your class.
All quadrilaterals form a family tree. Parallelograms are a group within quadrilaterals (they have two pairs of parallel sides). Rectangles and rhombuses are both special kinds of parallelograms. A square is the most specific: it is a parallelogram, a rectangle, AND a rhombus at the same time.
Trapezoids and kites are in the quadrilateral family too, but they are not parallelograms (they do not have two pairs of parallel sides).
Common Mistakes to Avoid
Mistake 1: Thinking a square is not a rectangle
A square IS a rectangle because it has four right angles and two pairs of equal, parallel sides. A square just has the extra property that all four sides are equal. Every square is a rectangle, but not every rectangle is a square.
Mistake 2: Thinking a rhombus is not a parallelogram
A rhombus IS a parallelogram because it has two pairs of parallel, equal sides. It just also has the extra property that all four sides are equal. Every rhombus is a parallelogram, but not every parallelogram is a rhombus.
Mistake 3: Forgetting that all quadrilateral angles sum to 360 degrees
This rule applies to every quadrilateral, no matter how unusual the shape. If you know three of the four angles, you can always find the fourth by subtracting from 360. This is a reliable test question strategy.
Common Questions About Quadrilaterals
What is a quadrilateral?
A quadrilateral is any closed polygon with exactly four sides, four angles, and four vertices. The four interior angles of any quadrilateral always add up to 360 degrees.
Is a rectangle a quadrilateral?
Yes. A rectangle is a quadrilateral with four right angles and two pairs of equal, parallel sides. All rectangles are quadrilaterals, but not all quadrilaterals are rectangles.
Is a square a rectangle?
Yes. A square is a special type of rectangle where all four sides are also equal. A square has all the properties of a rectangle plus the additional property of equal side lengths.
Is a rhombus a parallelogram?
Yes. A rhombus is a special parallelogram where all four sides are equal in length. Like all parallelograms, opposite sides are parallel and opposite angles are equal.
What is the difference between a rhombus and a square?
Both have four equal sides, but a square also has four right angles while a rhombus only requires that opposite angles be equal. Every square is a rhombus, but not every rhombus is a square.
How many sides does a quadrilateral have?
A quadrilateral has exactly four sides. The prefix quad means four in Latin. Examples include squares, rectangles, parallelograms, rhombuses, trapezoids, and kites.
