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.

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