Properties of Quadrilaterals
Purpose of the article:Hello Reader,
I see that you are looking to know about various types of quadrilaterals.
• Well, you have landed just at the right place.
In this article,
• You will get an idea about the quadrilateral and its various types.
• You will also get to know about the properties of a few special kinds of quadrilaterals.
So, let’s get straight into it.
What is a quadrilateral? A quadrilateral is a polygon that has 4 sides.
• So, any closed figure that has 4 sides is a quadrilateral.
• And, all the angles of a quadrilateral sum up to 3600.
The diagram given below shows a quadrilateral ABCD and the sum of its internal angles.
Various kinds of quadrilateralThere are some special kinds of quadrilateral that we see in our textbooks/ exams.
These are:
1. Rectangle
2. Square
3. Rhombus
4. Parallelogram
5. Trapezium
Let us discuss each type in detail.
RectangleA rectangle is a quadrilateral:
• Each of the 4 angles are \(90^o\)
• And, opposite sides of a rectangle are equal and parallel
• Diagonals of a rectangle bisect each other
Formulas to rememberIf the length of the rectangle is L and breadth is B then,
1. Area of a rectangle = Length × Breadth or L × B
2. Perimeter of rectangle = 2 × (L + B)
SquareA square is a quadrilateral:
• That has all the angles as \(90^o\)
• All sides of a square are equal
o And, opposite sides are parallel to each other
• Diagonals bisect each other perpendicularly
Formulas to rememberIf the side of a square is “a” then,
1. Area of the square = \(a × a = a^2\)
2. Perimeter of the square = 2 × (a + a) = 4a
ParallelogramA parallelogram is a quadrilateral in which:
• Opposite angles are equal
• Opposite sides are equal and parallel
• Diagonals bisect each other
• Sum of any two adjacent angles is \(180^o\)
Formulas to rememberIf the length of a parallelogram is “l”, breadth is “b” and height is “h” then:
1. Perimeter of parallelogram= 2 × (l + b)
2. Area of the parallelogram = l × h
RhombusA rhombus is a quadrilateral in which:
• Opposite angles are equal
• All sides are equal
o And, opposite sides are parallel to each other
• Diagonals bisect each other perpendicularly
• Sum of any two adjacent angles is \(180^o\)
Formulas to rememberIf the side of a rhombus is a then,
If the length of two diagonals of the rhombus is d1 and d2 then:
Area of the rhombus = \(\frac{1}{2} × d_1 × d_2\)
TrapeziumA trapezium is a quadrilateral in which:
• Only one pair of opposite sides are parallel to each other
Formulas to rememberIf the height of a trapezium is “h” (as shown in the above diagram) then:
Perimeter of the trapezium= Sum of lengths of all the sides = AB + BC + CD + DA
Area of the trapezium = \(\frac{1}{2}\) × (Sum of lengths of parallel sides) × h
= \(\frac{1}{2}\)× (AB + CD) × h
Summary of all the properties we learnt
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