Quadrilateral

Quadrilateral

A closed plane figure bounded by 4 sides or line segments is called a quadrilateral.

In the given figure, ABCD is a quadrilateral whose four sides are AB, BC, CD and AD. There are four interior angles in a quadrilateral and the sum of the angles of a quadrilateral is always 360°.

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Types of Quadrilateral

There are some special types of quadrilaterals. They are:

Rectangle: 

A quadrilateral having its opposite sides equal and each angle 90° is called a rectangle. ABCD in the given figure is a rectangle.

In a rectangle,

1.       Diagonals are equal and they bisect to each other.

2.       Opposite sides are equal and parallel.

Area of rectangle = l × b, where l is length and b is breadth of rectangle

Square: 

A quadrilateral having its all four sides equal and each angle 90° is called a square. ABCD in the given figure is a square.

In a square,

1.       Diagonals are equal and they bisect to each other at 90°.

2.       Opposite sides are equal and parallel.

Area of square = l², where l is length of square

Parallelogram: 

A quadrilateral having opposite sides parallel is called a parallelogram. ABCD in the given figure is a parallelogram.

In a parallelogram,

1.       Opposite sides are equal.

2.       Opposite angles are equal.

3.       Diagonals bisect each other.

Area of parallelogram = b × h, where b is base and h is height of parallelogram

Rhombus: 

A quadrilateral having its all four sides equal is called a rhombus. ABCD in the given figure is a rhombus.

In rhombus,

1.       Diagonals bisect to each other at 90°.

2.       Opposite sides are parallel.

3.       Opposite angles are equal.

Area of rhombus = ½ × d₁ × d₂, where d₁ and d₂ are diagonals of rhombus

Kite: 

A quadrilateral having its adjacent sides equal is called a kite. ABCD in the given figure is a kite.

In kite,

1.       Diagonals intersect each other at 90°.

Area of kite = ½ × d₁ × d₂, where d₁ and d₂ are diagonals of kite

Trapezium: 

A quadrilateral having a pair of its opposite sides parallel is called a trapezium. ABCD in the given figure is a trapezium.

Area of trapezium = ½ × h × (l₁ + l₂), where h is height and l₁ and l₂ length of parallel sides

You can comment your questions or problems regarding quadrilaterals here.