WHAT IS A QUADRILATERAL? WHAT ARE ITS PROPERTIES?

Properties of quadrilaterals	Rectangle	Square	Parallelogram	Rhombus	Trapezium
All Sides are equal	No	Yes	No	Yes	No
Opposite Sides are equal	Yes	Yes	Yes	Yes	No
Opposite Sides are parallel	Yes	Yes	Yes	Yes	Yes
All angles are equal	Yes	Yes	No	No	No
Opposite angles are equal	Yes	Yes	Yes	Yes	No
The sum of two adjacent angles is 180	Yes	Yes	Yes	Yes	No
Bisect each other	Yes	Yes	Yes	Yes	No
Bisect perpendicularly	No	Yes	No	Yes	No

Rectangle

The rectangle is a quadrilateral which has four right angles. The opposite sides of a rectangle are equal and parallel, and the diagonals bisect each other. Every angle in a rectangle is 90°.

(360°/4 = 90°).

 

The Properties of a rectangle are:

• Each angle is 90°
• The opposite sides are equal and parallel
• Diagonals in a rectangle bisect each other

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Formula: Area ad Perimeter of a rectangle

The length of the rectangle is L and the breadth of the rectangle is B.

Then, the Area of a rectangle= Length* Breadth

The perimeter of the rectangle= 2*(L+B)

Square

A square is a quadrilateral that has four equal angles and sides. Just like the rectangle, every angle in a square is 90° each.  

The three properties of a Square are:

• Every angle in a square is 90°
• All sides are equal and parallel to each other in a square
• Diagonals in a square bisect each other perpendicularly.

Formula –

Consider ‘a’ as the side of a square then,

The area of the square is given as a × a = a²

The perimeter of the square is given as 2 × (a + a) = 4a

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Parallelogram

A parallelogram is a quadrilateral and it has two pairs of parallel sides. The opposite angles are equal and the diagonals bisect each other in a parallelogram.

 

Properties of parallelogram

The opposite sides are equal and parallel

The diagonals in a parallelogram are equal and parallel

The sum of any two adjacent angles in a parallelogram is 180°

Consider the length of a parallelogram as ‘l’, breadth as ‘b’, and height as ‘h’ then:

The perimeter of parallelogram= 2*(l+ b)

Area of the parallelogram= l*h

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Rhombus

The Rhombus has four sides. The four sides are equal in length. The opposite sides are said to be parallel to each other. Rhombus is also designated as a diamond.

Properties of rhombus

The Opposite angles are equal in a Rhombus

All sides are equal. A rhombus has opposite sides that are parallel.

A rhombus has diagonals that bisect each other at 90 degrees.

The Sum of any two adjacent angles is 180° in a rhombus.

Formula– If ‘a’ is the side of a rhombus, then the perimeter of a rhombus= 4a

d1, d2 are the lengths of two diagonals in a rhombus, then the area of a rhombus= ½ × d1 × d2

Trapezium

The trapezium is also called a Trapezoid and it has only one pair of parallel sides. The parallel sides are designated as bases and the other two sides as lateral sides.

Properties of trapezium

Only one pair of opposite sides are parallel to each other in a trapezium.

The height of the trapezium in the above picture is given as ‘h&rsquo.

The perimeter of the trapezium= AB + BC + CD + DA

Area of the trapezium = ½ × (Sum of lengths of parallel sides) × h = ½ × (AB + CD) × h

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The most important formulas:

The below table represents the formulas for the area and perimeter of different types of quadrilaterals: