Types of Quadrilaterals, their properties, shapes, and areas

Types of Quadrilaterals, their properties, shapes, and areas

Quadrilateral properties, 6 types of quadrilateral, types of quadrilaterals chart, quadrilateral shapes, Trapezium, Parallelogram, Rectangle, Rhombus, Square, kite.

Family of Quadrilaterals

Quadrilateral :-

Any closed figure bounded by four sides is called a quadrilateral. A quadrilateral has four sides four vertices and four angles.

Properties of Quadrilateral:-
A quadrilateral have 4 sides, 4 vertices and 4 angles.
Sum of all angles of a quadrilateral is 360^o

$Area\: of\: quadrilateral\: =\frac{1}{2}\times AC(DE+BF)$

Trapezium:-

If one pair of opposite sides of a quadrilateral is parallel then it is called a trapezium.

Properties of Trapezium

One pair of opposite sides are parallel.

Two pair of adjacent angles are supplementary.

$Area\: of\: trapezium=\frac{1}{2}\times (b_{1}+b_{2})\times h$

Parallelogram:-

If both pair of opposite sides of a quadrilateral is parallel then the quadrilateral is a parallelogram.

If one pair of opposite sides of a quadrilateral is equal and parallel then the quadrilateral is a parallelogram.

If both pair of opposite sides of a quadrilateral are equal and diagonals are not equal then the quadrilateral is a parallelogram.

Properties of parallelogram

Opposite sides are equal and parallel.

Opposite angles are equal.

Adjacent angles are supplementary.

Diagonals bisect each other.

Diagonals are not equal.

Area of parallelogram = Base x Height

Rectangle:-

If one angle of a parallelogram is right then it is called a rectangle.

If both pair of opposite sides of a quadrilateral are equal and diagonals are also equal then the quadrilateral is a rectangle.

Properties of Rectangle

Both pair of opposite sides are equal and parallel.
Diagonals are equal and bisects each other.
All angles are equal to 90^o
Adjacent angles are supplementary.

Area of rectangle = Length X Breadth

Rhombus:-

If adjacent sides of a parallelogram are equal then it is called a rhombus.
If all sides of a quadrilateral are equal and diagonals are not equal then the quadrilateral is a rhombus.

Properties of Rhombus:-

All sides are equal.
Opposite sides are equal and parallel.
Opposite angles are equal.
Adjacent angles are supplementary.
Diagonals bisects each other at right angle.
Diagonals are not equal.
Area of Rhombus = Base x Height.
$Area\: of\: Rhombus\: =\frac{1}{2}\times Product\: of\: diagonals$
$Area\: of\: Rhombus\: =\frac{1}{2}\times d_{1}\times d_{2}$

Square:-

A parallelogram whose one angle is right and adjacent sides are equal is called a square.

A rectangle whose adjacent sides are equal is called a square.

A rhombus whose one angle is right is called a square.

If all sides of a quadrilateral are equal and diagonals are also equal then the quadrilateral is a square.

Properties of Square

All sides are equal.
All angles are equal to 90^o
Diagonal are equal.
Adjacent angles are supplementary.
Opposite side are equal and parallel.
Opposite angles are equal.
Perimeter of square is = 4 x side
Area of Square is = (side x side)
$Area\: of\: Square\: =\frac{1}{2}\times d_{1}\times d_{2}$
$Area\: of\: Square\: =\frac{1}{2}\times product\: of\:diagonals$

Kite

If two pair of adjacent sides of a quadrilateral is equal then the quadrilateral is a kite.

Properties of Kite

Two pairs of adjacent sides are equal.
Diagonals are perpendicular to each other.
One diagonal bisect the other.

$Area\: of\: kite\: =\frac{1}{2}\times d_{1}\times d_{2}$

Type	Figure	Perimeter	Area
Quadrilateral		Sum of four sides	$\frac{1}{2}\times AC[DE+BF]$
Trapezium		Sum of four sides	$\frac{1}{2}\times (b_{1}+b_{2})\times h$
Parallelogram		Sum of four sides	Base x Height
Rectangle		2 (Length + Breadth)	Length x Breadth
Rhombus		4 x Side	$\frac{1}{2}\times d_{1}\times d_{2}$
Square		4 x Side	$=side\times side\\\\ \: \:\: \: \: \: =\frac{1}{2}\times d_{1}\times d_{2}$
Kite		Sum of 4 sides	$\frac{1}{2}\times d_{1}\times d_{2}$