A quadrilateral is a shape with four sides, four angles, and four corners. The name comes from the Latin words "quadri," which means four, and "latus," meaning side. So, any closed figure with four sides is a quadrilateral. The total of interior angles in a quadrilateral is always 360 degrees.There are different types of quadrilaterals, each with its own unique features related to sides, angles, and symmetry.
Table of Contents
Each type of quadrilateral has its own properties. However, some properties apply to all quadrilaterals:
A quadrilateral always has four sides and four angles.
The sum of all internal angles in a quadrilateral is always 360 degrees.
A quadrilateral can have equal or unequal sides and angles.
Some quadrilaterals have opposite sides that are parallel or equal.
The diagonals, which are the lines joining opposite corners, behave in specific ways depending on the type of quadrilateral. They may bisect each other, be equal in length, or intersect at right angles.
These are the basic properties of a quadrilateral. When we move on to the specific types of quadrilaterals, each has its special set of properties.
There are six main types of quadrilaterals:
Parallelogram
Trapezium
Rhombus
Rectangle
Square
Kite
Each of these types of quadrilaterals has a distinct shape, property, and formula for calculating the area. Let us explore each one in detail.
A parallelogram is a specific kind of quadrilateral where opposite sides are parallel and the same length. The opposite angles are equal, and the diagonals cut each other in half. This is one of the most common types of quadrilaterals and is often used in building and design.
Properties of a Parallelogram:
Opposite sides are parallel and equal.
Opposite angles are equal.
Diagonals bisect each other.
Adjacent angles are supplementary; they add up to 180 degrees.
Area of a Parallelogram = base × height.
The parallelogram is a useful shape in geometry. Understanding its properties is important for solving problems related to angles, sides, and area. Among quadrilaterals, the parallelogram helps us understand rectangles and rhombuses.
A trapezium is a quadrilateral with one pair of opposite sides that are parallel. These parallel sides are called the bases. The other two sides are known as non-parallel sides or legs. This shape adds to the variety of quadrilaterals.
Properties of a Trapezium:
One pair of opposite sides is parallel.
The non-parallel sides can be equal, as seen in an isosceles trapezium.
The angles on the same side of a leg are supplementary.
Diagonals may or may not be equal.
Area of a Trapezium = 1/2 × (sum of parallel sides) × height
The trapezium is particularly useful in architectural designs, ramps, and artistic patterns. Among the types of quadrilaterals, the trapezium is special because it has only one pair of parallel sides.
A rhombus is a type of quadrilateral where all four sides have the same length. It is similar to a square but doesn't need right angles. The diagonals of a rhombus cross each other at 90 degrees and cut each other in half.
Properties of a Rhombus:
All sides are equal in length.
Opposite angles are equal.
Diagonals cross each other at right angles.
Diagonals cut the interior angles in half.
Area of a Rhombus = (diagonal1 × diagonal2) / 2.
A rhombus is often seen as a tilted square. It appears in art and design because of its symmetry. Knowing the properties of a rhombus helps students tell it apart from squares and other quadrilaterals.
A rectangle is a four-sided shape with four right angles. Its opposite sides are equal and run parallel to each other. The diagonals of a rectangle are equal and cut each other in half. The rectangle is one of the most common types of four-sided shapes.
Properties of a Rectangle:
All angles are right angles (90 degrees).
Opposite sides are equal and parallel.
Diagonals are equal and bisect each other.
Area of a Rectangle = length × breadth
Rectangles are found everywhere: in notebooks, mobile screens, doors, windows, and tables. Because of its simple shape and easy area formula, it is one of the most frequently used types of quadrilaterals.
A square is a special type of rectangle and rhombus where all sides are equal and all angles are 90 degrees. It is the most regular and symmetric type among all types of quadrilaterals.
Properties of a Square:
All four sides are equal.
All four angles are right angles.
Diagonals are equal in length and bisect each other at 90 degrees.
Area of a Square = side × side
The square combines the properties of a rectangle and a rhombus. It is the most symmetric of all types of quadrilaterals. Squares are widely used in tiling, design, and measurement.
A kite is a quadrilateral with two distinct pairs of adjacent sides that are equal. One pair of opposite angles are equal, and its diagonals intersect at right angles. One diagonal bisects the other.
Properties of a Kite:
Two pairs of adjacent sides are equal.
One pair of opposite angles are equal.
Diagonals intersect at right angles.
One diagonal bisects the other.
Area of a Kite = (diagonal1 × diagonal2) / 2
Kites are commonly seen in toy shapes, logos, and ornaments. Among the types of quadrilaterals, the kite is unique due to its adjacent side properties and diagonal relationships.
Among all types of quadrilaterals, the kite is unique in having no parallel sides but still strong symmetry.
Example 1: Find the area of a trapezium whose bases are 10 cm and 14 cm, and height is 6 cm.
Area of trapezium = ½ × (Base₁ + Base₂) × Height
= ½ × (10 + 14) × 6
= ½ × 24 × 6
= 12 × 6
= 72 cm²
Example 2: A rectangle has length = 8 cm and breadth = 5 cm. Find its area.
Area of rectangle = Length × Breadth
= 8 × 5
= 40 cm²
Example 3: Find the area of a rhombus with diagonals 10 cm and 8 cm.
Area of rhombus = ½ × Diagonal₁ × Diagonal₂
= ½ × 10 × 8
= 5 × 8
= 40 cm²
Example 4: A square has side = 9 cm. Find the area.
Area of square = Side × Side
= 9 × 9
= 81 cm²
Example 5: Find the area of a kite with diagonals 6 cm and 10 cm.
Area of kite = ½ × Diagonal₁ × Diagonal₂
= ½ × 6 × 10
= 3 × 10
= 30 cm²
Example 6: A parallelogram has base = 12 cm and height = 7 cm. Find its area.
Area of parallelogram = Base × Height
= 12 × 7
= 84 cm²
Example 7: Find the area of a trapezium with base₁ = 9 cm, base₂ = 7 cm, and height = 6 cm.
Area of trapezium = ½ × (Base₁ + Base₂) × Height
= ½ × (9 + 7) × 6
= ½ × 16 × 6
= 8 × 6
= 48 cm²
Example 8: A kite has diagonals 5 cm and 9 cm. Find the area.
Area of kite = ½ × 5 × 9
= 2.5 × 9
= 22.5 cm²
The study of quadrilaterals is a basic part of geometry. A square is regular, a kite is unique, a rectangle is symmetrical, and a parallelogram has a slanted elegance. Each shape has its own properties and formulas.
Understanding the properties of a quadrilateral aids in recognizing how these shapes work in math and in real life. Calculating the area of quadrilaterals is crucial in fields like architecture, construction, and design.
Practicing with examples and area formulas for quadrilaterals builds understanding and confidence in identifying different types of quadrilaterals.
Related Links
Quadrilateral - Explore more about quadrilaterals with clear explanations and examples.
Parallelogram - Learn all about parallelograms with simple explanations.
Triangles - Discover the types and properties of triangles in an easy way.
The 7 types of quadrilaterals are:
Square
Rectangle
Rhombus
Parallelogram
Trapezium
Kite
Irregular Quadrilateral
Each of these quadrilaterals has four sides but different properties such as angle measures, symmetry, and side lengths. These types are commonly used in geometry to classify and solve various shape-related problems.
The six main types of quadrilaterals are:
Square
Rectangle
Rhombus
Parallelogram
Trapezium
Kite
These are the most basic and commonly studied quadrilaterals in school-level geometry. Each has unique characteristics based on the equality and parallelism of sides and angles.
The seven main properties of a quadrilateral are:
It has four sides
It has four vertices
The sum of the interior angles is 360 degrees
It has two diagonals
Some types have equal opposite sides
Some types have parallel opposite sides
Diagonals may bisect each other, intersect perpendicularly, or be equal depending on the type
These properties help identify and differentiate between various types of quadrilaterals.
The 12 types of angles commonly covered in class are:
Acute Angle (less than 90°)
Right Angle (exactly 90°)
Obtuse Angle (between 90° and 180°)
Straight Angle (exactly 180°)
Reflex Angle (between 180° and 360°)
Complete Angle (exactly 360°)
Adjacent Angles
Complementary Angles
Supplementary Angles
Vertically Opposite Angles
Interior Angles
Exterior Angles
These angle types are fundamental in geometry and are especially important when working with polygons and shapes like quadrilaterals.