Properties of Rectangle

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Basic Properties of Rectangle

Rectangle is a plane, geometrical figure which is also one type of a quadrilateral. This geometrical figure is often spotted in our day-to-day life in the form of a storage box, painting, slab etc. Rectangle holds its own significance when it comes to menstruation and geometry. 

The word rectangle has its origin from the Latin word rectangulus, which is again extracted from two words i.e. – rectus, that means right or appropriate and angulus, means angle. It is evident from the name itself that a rectangle has right angles. 


Properties of Rectangle in Points

To get a better understanding of rectangles and its properties, let’s take a look at the characteristics and all properties of rectangles.

Below is a clear depiction of characteristics of the rectangle and its properties.

  • A rectangle is a type of a quadrilateral

  • The opposite sides are equal and parallel.

  • It has 4 equal internal angles which measures 90° each.

  • rectangle is also a parallelogram because the opposite angles of a rectangle are equal

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Properties of Diagonals of Rectangle

The properties of diagonals of rectangle is hereunder:

  • The diagonals of a rectangle are of the same length and intersect one another

  • The two diagonals of a rectangle intersect each other at different angles – one acute angle and the other an obtuse angle.

  • A rectangle whose two diagonals intersect each other at right angles is known as a square.

  •  While the 2 equal diagonals of a rectangle intersect each other, the 4 vertices of a rectangle are at equal distance from the point of intersection.

  • Because of the equidistance from the point of intersection, a circumcircle can be formed with its center at the point of intersection of the diagonals and its circumference crossing across the 4 vertices of the rectangle.

  • The diameter of the circumcircle formed is equivalent to the diagonal of the rectangle.

Properties of a Special Case of Parallelogram: Square 

You will find the below given attributed in square.

  • All the properties of a rectangle apply (the only one that matters here is diagonals are congruent).

  • All sides are equal in length that also means all sides and opposite sides are congruent to each other 

  • All angles forms right angles which means 90 degrees each 

  • The diagonals are perpendicular bisectors of each other, and also intersect the angles

Note: All the properties of a rhombus are also applicable to a square (the ones that are for consideration here are parallel sides, diagonals bisection).


Solved Examples

Example 1: If the Length and the Width of a Rectangular Box are 7 cm and 4 cm Respectively. Calculate the Area and Perimeter of the Box.

 

Solution:

Given,

length of the rectangle, a = 7 cm

Width of the rectangle, b = 4 cm.

Thus, applying the area of rectangle i.e. = length × width, we get

= (7 × 4) cm2 = 28 cm2.

Now, formula for Perimeter of a rectangle = 2 (Length + Width)

= 2 (7 + 4) = 2 × 11 = 22 cm.

 

Example 2: We are Given the Width and Diagonal of a Rectangle to be 9 cm and 15 cm Respectively. Find out its Length.

 

Solution:

Given that,

Width of the rectangle, = 9 cm

Diagonal of the rectangle, = 15 cm

Applying the formula:  (Diagonal) 2 = (Length) 2 + (Width) 2.

Thus, we have,

152 = a2 + 92

=> a2 = 152 – 92 

= 225 – 81 = 144

=> l = 144 = 12 cm.

FAQ (Frequently Asked Questions)

Q1. What is a Rectangle?

Answer: A rectangle is a 2-D geometrical figure which comprises four sides, four angles and four vertices. The opposite sides of a rectangle are equal in measurement and are also parallel to each other. In addition, the internal angles of a rectangle are equal and measure 90° each.


What is amongst the special properties of a rectangle is that it’s also a parallelogram. There are 3 special parallelograms namely— rectangle, rhombus, and square. Moreover, the square is a special type or case of both the rectangle and the rhombus.

Q2. What are Various Other Types of Quadrilaterals than Rectangles?

Answer: Besides rectangle, we have other types of quadrilaterals such as:

  • Parallelogram

  • Square

  • Rhombus

  • Trapezoid

  • Isosceles Trapezoid

  • Kite

Note that squares and rectangles are much easier to deal with when it comes to solving questions than the rest of the others quadrilaterals.

Q3. What are the Properties of a Rhombus?

Answer: A rhombus consists of the following properties:

  • All sides are congruent to each other

  • The diagonals intersect the angles.

  • The diagonals of a rectangle are also the perpendicular bisectors of each other

Note: All the properties of a parallelogram are applicable to rhombus (the ones that consider here are parallel sides, congruence of opposite angles, and supplementary consecutive angles).

Q4. What is the Formula to Calculate the Area of a Rectangle?

Answer: Area of a Rectangle = a×b [length × breadth]