Rectangle

Rectangle Information

Shapes are the base for everything today. Look at the things around you. The television, phone, the utensils you use to cook food every day, everything has a shape around you. In this section, we shall be talking about the rectangle. So, what is the rectangle shape? The rectangle information that is stated in this article is for the better undertaking of the shape. A rectangle has four-sided and all the internal angles are equal to 90 degrees. The length of the opposite sides of the rectangle is always equal to each other. If all the sides are equal then it is square. For example: Let us say the lengths of a rectangle are 10 m and the width is 20 m, then the rectangle would look like the image shown below: (image will be updated soon)


Now, let us learn about the sides of the rectangle. The rectangle’s sides are the length (L) and the width (W). Look at the image above. You notice that the rectangle has four sides - PQ, QR, RS, and SP and all the angles \[\angle P,\angle Q,\angle R,{\text{ }}and{\text{ }}\angle S\]. The distance between P and Q is the length (L) of the rectangle and the distance between P and S is called the width (W) of the rectangle.


Some Real-World Applications of the Rectangle Shape.

  • Book

  • Television 

  • Mobile Phone

  • A4 Sheet

  • A tennis court


The Perimeter of a Rectangle

Now that we learned the definition of a rectangle in maths, let’s learn about the perimeter of the rectangle. 


The total distance that is covered by the rectangle is called the perimeter of the rectangle. 


In Mathematics, the perimeter of a rectangle goes by:


The perimeter of a rectangle ( P ) = ( Length of the rectangle + Width of the triangle ) \[ \times \]2


Therefore,


\[P = 2\left( {{\text{ }}l + w} \right){\text{ }}unit.\]


The Area of a Rectangle

 

The total space occupied by a rectangle is called the area of a rectangle.


In Mathematics, the area of a rectangle goes by:


The area of a rectangle ( A ) = Length of a rectangle ( L ) \[ \times \] Width of a rectangle ( W )


Therefore,


\[A = L \times W{\text{ }}uni{t^2}.\]


Properties Of a Rectangle

To know the properties of a rectangle, you should have the basic knowledge of a rectangle. We learned that a rectangle has four-sided and all the internal angles are equal to 90 degrees. The length of the opposite sides of the rectangle is always equal to each other. A rectangle has four-sided and all the internal angles are equal to 90 degrees. The length of the opposite sides of the rectangle is always equal to each other. If all the sides are equal then it is square. Listed below are the properties of a rectangle.


  • A rectangle is a parallelogram with four 90 degree angles. 

  • The diagonals of a rectangle bisect each other.

  • The sides in a rectangle are always equal to each other.

  • The sides opposite to each other are always parallel to each other

  • The perimeter of a rectangle \[P = 2\left( {{\text{ }}l + w} \right)\]; L is the breadth and W is the width

  • The area of a rectangle \[A = 2\left( {L*W} \right)\]; L is the breadth and W is the width

  • When all the angles are added together, then the sum of all the angles of a rectangle = 360 degrees

  • The diameter circumference of a rectangle is the diagonals of a rectangle


Diagonals of a Rectangle (image will be updated soon)

There are two diagonals in a rectangle. They have equal lengths and intersect right in the center. Look a the picture above to understand it better. 


Now, to find the length of the diagonal use the formula given below:


\[D = \sqrt {{L^2} + {W^2}} \]


Solved Examples

Question 1: The sides of a rectangle are 3 cm  and 4 cm. Find the area, the perimeter, and the length of the diagonals of the rectangle. 

Solution: 

Given, 


Length of the rectangle ( L ) = 3 cm


Width of the rectangle ( W ) = 4 cm


Area of a rectangle ( A ) = L \[ \times \]W


Therefore,


Area of the rectangle ( A ) = 3 \[ \times \] 4


Area of the rectangle ( A ) = 12 \[c{m^2}\]


The perimeter of the rectangle ( P ) = 2 ( L + W )


Therefore,


The perimeter of the rectangle ( P ) = 2 ( 3 + 4)


The perimeter of the rectangle ( P ) = 2 ( 7 )


The perimeter of the rectangle ( P ) = 14 cm.


The length of the Diagonal, 


\[D = \sqrt {{L^2} + {W^2}} \]

  \[D = \sqrt {{3^2} + {4^2}} \]

  \[D = \sqrt {9 + 16} \]

  \[D = \sqrt {25} \]

D = 5 cm


Question 2: The sides of a rectangle are 5 cm  and 12 cm. Find the area, the perimeter, and the length of the diagonals of the rectangle. 

Solution: 


Given, 


Length of the rectangle ( L ) = 5 cm


Width of the rectangle ( W ) = 12 cm


Area of a rectangle ( A ) = L \[ \times \] W


Therefore,


Area of the rectangle ( A ) = 5 \[ \times \]12


       = 60 cm2


The perimeter of the rectangle ( P ) = 2 ( L + W )


Therefore,


The perimeter of the rectangle ( P ) = 2 ( 5 + 12)


The perimeter of the rectangle ( P ) = 2 ( 17 )


          = 34 cm.


The length of the Diagonal, 


\[D = \sqrt {{L^2} + {W^2}} \]


\[D = \sqrt {{5^2} + {12^2}} \]

  \[D = \sqrt {25 + 169} \]

  \[D = \sqrt {169} \]

D = 13 cm