In this post we will discuss properties and formulas of different quadrilateral in detail.
Following quadrilaterals are discussed below;
(a) Square
(b) Rectangle
(c) Parallelogram
(d) Rhombus
(e) Trapezium
Along with the properties, try to remember all the formulas as they would help you solve related questions in examination.
Square
The square has following properties;
(a) All sides are equal
(b) All angle measures 90 degree
(c) Diagonals bisect each other at 90 degree
Given above is the square ABCD in which;
(i) All sides are equal
AB = BC = CD = DA
(ii) All angle measure 90 degree
∠A = ∠B = ∠C = ∠D = 90 degree
(iii) Diagonals bisect each other
AO = OC and Bo = OD
(iv) Diagonals intersect at right angle
∠AOB = 90
Formula for Square
Area of square = side x side
Perimeter of square = 4 x side
Rectangle
The rectangle has following properties;
(a) All angle measures 90 degree
(b) Opposite sides are equal and parallel
(c) Diagonal bisect each other
Given above is the rectangle ABCD in which;
(i) ∠A = ∠B = ∠C = ∠D = 90 degree
(ii) Opposite sides are equal & parallel
AB = CD and AD = BC
(iii) Diagonals bisect each other
AO = OC and DO = OB
Rectangle Formulas
Area of Rectangle = Length x Breadth
Perimeter of Rectangle = 2 (Length + Breadth)
Parallelogram
As the name suggests, it’s a quadrilateral whose opposite sides are parallel to each other.
The parallelogram has following properties;
(a) Opposite sides are equal and parallel
(b) Opposite angles are equal
(c) Diagonals bisect each other
(d) Sum of adjacent angle is 180 degree
Since all the properties are similar to rectangle, what’s the difference between the quadrilateral rectangle and parallelogram?
In rectangle, all angle measures 90 degree but such is not the case with parallelogram.
Given above is the parallelogram ABCD in which;
(i) Opposite sides are equal
∠A = ∠C and ∠D = ∠B
(ii) Opposite sides are equal and parallel
AD = BC and AB = CD
(iii) Diagonals bisect each other
AO = OC and DO = OB
(iv) Sum of adjacent angle is 180 degree
∠A + ∠D = 180 degree
Parallelogram formulas
Area of parallelogram = Length x Height
Perimeter of parallelogram = 2 (length + breadth)
Rhombus
Rhombus is a quadrilateral that looks like a diamond.
The Rhombus have following properties;
(a) All sides are equal
(b) Opposite sides are parallel to each other
(c) Opposite angles are equal
(d) Diagonal bisect each other at 90 degree
(e) Sum of adjacent angle measures 180 degree
What’s the difference between a square and a rhombus ?
In square, all angle measures 90 degree but such is not the case with rhombus.
If you make all the angle of rhombus 90 degree then it will become square.
Given above is the Rhombus ABCD in which;
(a) All sides are equal
AB = BC = CD = DA
(b) Opposite angles are equal
∠A = ∠C and ∠B = ∠D
(c) Diagonals bisect each other at 90 degree
∠AOB = 90 degree
Rhombus Formula
Area of Rhombus = 1/2 x d1 x d2
where d1 & d2 are length of diagonals
Perimeter of rhombus = 4 x length
Trapezium
Trapezium is a quadrilateral in which one pair of sides are parallel while other pair are non parallel to each other.
Given below are important formulas for trapezium;
Area of Trapezium = 1/2 x (AB + CD) x height
Perimeter of trapezium = AB + BC + CD + DA