A quadrilateral is a two-dimensional shape with 4 sides. Here you will find examples of various quadrilateral 4-sided shapes as well as definitions, types, examples, and all special properties of quadrilaterals. Let’s get started now!
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What is a quadrilateral shape?
A quadrilateral is a four-sided and two-dimensional shape. Squares, rectangles, and kites are all examples of quadrilaterals. ‘Quad’ refers to four, and ‘lateral’ refers to sides.
A quadrilateral can be regular or irregular, which means that its sides do not need to be the same length or angle. A shape must be 2D, closed, and also have 4 straight sides to be classified as a quadrilateral.
Quadrilaterals always have 4 sides, 4 vertices, and 4 interior angles totaling 360°.
A quadrilateral is a plane figure formed by four line segments that form a space. Building your own quadrilateral is the quickest and easiest way to learn about them.
Find 4 straight objects that can be used as line segments (four = quadr; side = lateral). Straws, rulers, dowels, pens, or whatever else you have on hand will suffice; they do not need to be of the same length. A quadrilateral, or four-sided polygon, is formed by connecting the four linear objects at their eight ends.
Perhaps you arranged four sides so that the shape appears full, indicating that you created a convex quadrilateral. Perhaps your four line segments formed a pointy shape like an arrowhead; perhaps you formed a concave quadrilateral.
Typically, the four sides do not cross, resulting in a simple quadrilateral. You can make a complex quadrilateral by arranging your quadrilateral so that line segments cross each other.
Types of Quadrilaterals
Concave Quadrilaterals
Concave quadrilaterals are quadrilaterals with one interior angle larger than 180° and one diagonal outside the quadrilateral. A Dart is an example of a concave quadrilateral. Like a kite, it is a quadrilateral with bilateral symmetry and a reflex interior angle.
In the photo below, one of the quadrilateral’s interior angles (C) is greater than 180°. As a result, the quadrilateral has a concave shape.
Convex Quadrilaterals
Concave quadrilaterals are quadrilaterals with all 4 interior angles smaller than 180°. Convex Quadrilaterals are classified into several types:
- Trapezoid
- Kite
- Parallelogram
- Rectangle
- Rhombus
- Square
Properties of Quadrilateral
Each of the quadrilaterals mentioned above has its own set of properties. However, some properties are shared by all quadrilaterals. They are listed below.
- They have 4 sides.
- They have 4 vertices.
- They have 2 diagonals.
- The total of all interior angles equals 360°.
We will investigate the other properties of various quadrilaterals in depth. We can classify a quadrilateral based on the quadrilateral properties listed below.
Square Properties
All of the square’s sides are the same length.
A square’s sides are parallel to one another, and all of its interior angles are 90 degrees (i.e., right angle)
The diagonals of a square perpendicular cross each other
Rectangle Properties
A rectangle’s opposite sides are all the same length.
The opposing sides are perpendicular to each other.
A rectangle’s interior angles are all 90 degrees.
A rectangle’s diagonals cross each other.
Rhombus Properties
A rhombus’s 4 sides are all the same size.
The opposite sides of the rhombus are parallel, and the opposite angles are the same size.
The total of any two adjacent rhombus angles equals 180 degrees.
The diagonals are perpendicular to each other.
Parallelogram Properties
The parallelogram’s opposite side is the same length.
The opposing sides are perpendicular to each other.
A parallelogram’s diagonals cross each other.
The opposite angles are equal.
The total of 2 adjacent parallelogram angles equals 180 degrees.
Properties of Trapezium
A trapezium has only one pair of opposite sides that are parallel to each other.
A trapezium’s 2 adjacent sides are supplementary (180 degrees)
A trapezium’s diagonals cross each other in the exact same ratio.
Properties of Kite
A kite’s two adjacent sides have the same length.
A kite’s largest diagonal cuts through the smallest diagonal.
Only 1 pair of opposite angles has the same length.
Area of Quadrilaterals
A quadrilateral’s area is measured by the amount of space covered by a quadrilateral in two dimensions. The area of each type of quadrilateral is calculated using a different formula. The formula to calculate the area of each type of quadrilateral is shown in the table below:
| Area of a Parallelogram | Base x Height | |||
|---|---|---|---|---|
| Area of a Rectangle | Length x Width | |||
| Area of a Square | Side x Side | |||
| Area of a Rhombus | (1/2) x Diagonal 1 x Diagonal 2 | |||
| Area of a Kite | 1/2 x Diagonal 1 x Diagonal 2 |
Perimeter of Quadrilaterals
A quadrilateral’s perimeter is the total value of its sides. The perimeter formula differs for different quadrilateral shapes because they exhibit different properties. The formulas for various quadrilateral shapes are provided below.
| Quadrilateral Name | Perimeter | |||
|---|---|---|---|---|
| Square | 4 x Side | |||
| Rectangle | 2(Length + Breadth) | |||
| Parallelogram | 2(Base + Side) | |||
| Rhombus | 4 x Side | |||
| Kite | 2 (a + b), where a and b are adjacent pairs. |
In primary school, what do children learn about quadrilaterals?
- Children in Year 1 will be taught the names of 2D shapes like rectangles and squares. They may be shown 3D shapes and asked to determine whether the faces are rectangular or square.
- In Year 2, students will begin to investigate symmetry in rectangular and square shapes. They will be required to draw symmetry lines on these shapes.
- Children in Year 3 may be required to draw 2D shapes like squares and rectangles. They will also begin to learn about right angles and, as a result, will understand that each rectangle and square has four right angles. They will also be taught the terms parallel and perpendicular, as well as how to recognize parallel and perpendicular lines in some quadrilaterals.
- In Year 4, learners acquire the term quadrilateral and are tasked with determining whether or not a given shape is a quadrilateral.
- In Year 5, students will be required to draw shapes that meet specific requirements (for example: draw a quadrilateral with an obtuse angle and a right angle). They will also be required to use their quadrilateral understanding to identify missing lengths and angles.
- In Year 6, students learn that the internal angles of a quadrilateral add up to 360 degrees. This knowledge will be used to find missing angles in quadrilaterals.
What are real-life examples of quadrilaterals?
A quadrilateral is defined as any shape with four equal sides. Examples include a tabletop, book, tablet, picture frame, television, kite, and so on.
How many sides does a quadrilateral have?
A quadrilateral is made up of four straight sides. Sides and angles can have equal or unequal lengths. Special types of quadrilaterals, such as squares and rectangles, are formed when 2 or 4 sides are equal.
Two quadrilateral sides could cross each other to form a complex quadrilateral, which looks like two adjoining triangles.
What is a simple quadrilateral?
Simple quadrilaterals can be concave or convex. That is, the interior angles of a simple (and planar) quadrilateral ABCD total 360 degrees of arc. S = (n 2) 180° is a special case of the n-gon interior angle sum formula.
Why are all quadrilaterals 360?
A quadrilateral is a polygon with four vertices and four sides enclosing four angles, the total value of which is 360°. When we draw diagonals to a quadrilateral, we get two triangles. The sum of these triangles’ angles is 180°. As a result, the quadrilateral’s total angle sum is 180 + 180 = 360°.
Is a square a quadrilateral?
Squares are quadrilaterals with four congruent sides, four right angles, and 2 pairs of parallel sides.
If you are planning to teach your kids about this essential topic, you can make your own collections of quadrilateral worksheets using our worksheet maker.
