A closed geometric figure with four sides and four vertices is called a quadrilateral. The sum of all the four angles of a quadrilateral is 360°.

A quadrilateral can be classified as follows.

(i) Square

(ii) Rectangle

(iii) Parallelogram

(iv) Rhombus

Square :

A square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted ABCD. ## Properties of square

• All four sides of a square are same length, they are equal
• Opposite side of a square are parallel
• All four angles of a square are right angles
• Sum of the angles of a square are equal to 360 degree.
• Diagonals of a square are same length
• Each diagonal of a square divides its into  two equal symmetrical area.
• Diagonals of a square intersect its right angles, and share each other half.

Area of a square  =  a²

Perimeter of a square  =  4 a

Here "a" stands for side length of the square.

Rectangle :

A rectangle is a quadrilateral with four right angles. It can also be defined as an equiangular quadrilateral, since equiangular means that all of its angles are equal. ## Properties of rectangle

• An opposite sides of a rectangle are the same length, they are equal
• An opposite sides of a rectangle are parallel
• An adjacent sides of a rectangle are always perpendicular
• All four angles of a rectangles is right.
• The sum all of the angles of a rectangle is equal to 360 degrees.
• The diagonals of a rectangle are equal
• The sum of squares two diagonals is equal to the sum of squares of the sides.

Area of the rectangle  =  length x width

Perimeter of the rectangle  =  2(length  + width)

Parallelogram :

A quadrilateral in which the opposite sides are parallel is called a parallelogram. • Opposite sides are parallel and equal.
• Opposite angles are equal and sum of any two adjacent angles is 180°.
• Diagonals bisect each other.
• The sum of the parallelogram angles is equal to 360 degrees.
• Each diagonals divides the parallelogram into two equal triangle.
• Two diagonals is divided parallelogram into two pairs of equal triangles.

Area of parallelogram  =  base x height (or)

Area of parallelogram  =  diagonal 1 x diagonals 2

Perimeter of parallelogram  =  Sum of length of all sides

Rhombus :

A rhombus is a simple quadrilateral whose four sides all have the same length. • All sides are equal and opposite sides are parallel
• Opposite angles are equal and sum of any two adjacent angles is 180°.
• Diagonals bisect each other at right angles.
• The intersecting point of the diagonals is the center of the symmetry.
• At any rhombus can be inscribed a circle.

Area of rhombus  =  (1/2)(diagonal 1 x diagonals 2)

Perimeter of rhombus  =  Sum of length of all sides After having gone through the stuff given above, we hope that the students would have understood "Classify quadrilaterals".