Perimeter

Let’s start the topic with a small activity.

Step 1: Measure all the sides of your table or handkerchief using ruler.

Step 2: Calculate the sum of the length of all sides.

Step 3: Write the final calculated measurement. The final answer we got is the total length of the boundary. The length of the boundary is known as perimeter.

Therefore, perimeter means distance around a figure or curve. We can only measure perimeter of a closed figure/2 dimensional shape or curve as movement around a closed figure or curve is possible.

Example: We cannot move around the below figure.

If we start our journey from point A, we will reach point C but cannot reach back to point A as it is open figure.

Perimeter of a Square

A square is a closed figure that has 4 sides of equal length and 4 equal angles of 90 degree.

Perimeter of a square

= sum of all sides

OR                               

= 4 x Side

Example: Side of square 10 cm

Method 1: Perimeter = 10 + 10 + 10 + 10 (sum of all 4 sides)

                               = 40 cm

Method 2: As all sides are equal we can write 4 times side in place of adding all sides.

              Perimeter = 4 x 10 cm

                             = 40 cm

Perimeter of a Rectangle

A rectangle is a closed figure that has equal opposite sides and each angle is of 90 degree. The longer side of rectangle is known as length of the rectangle and shorter side is known as width or breadth of rectangle.

Perimeter of Rectangle

= L + L + B + B

OR

=2 X L + 2 X B (i.e. 2L + 2B)

OR

=2 (L + B) (taking 2 common i.e. twice the sum of length and breadth)

Example: Length =10cm and Breadth = 5cm

Method 1: Perimeter = 10 + 10 + 5 + 5 (sum of all 4 sides)

                               = 30 cm

Method 2: As opposite sides are equal we can write sum 2 times length and 2 times breadth.

Perimeter = 2 X L + 2 X B (i.e. 2L + 2B)

              = 2 x 10 + 2 x 5

              = 20 + 10

              = 30 cm

OR

Perimeter = 2 (L + B)

               = 2 (10 + 5) (solve bracket first)

               = 2 X 15

               = 30 cm

Perimeter of a Triangle

Scalene Triangle - A triangle whose all three sides are of different length and all 3 angle are of different measurement is known as scalene triangle.

Perimeter of Scalene Triangle = Side 1 + Side 2 + Side 3

Example:

Perimeter = AB + BC + CA

               = 5 cm + 10 cm + 12 cm

               = 27 cm

Isosceles Triangle - A triangle whose two sides are of equal length and 2 angle are of equal measurement is known as isosceles triangle.  

Perimeter of Isosceles Triangle = Side 1 + Side 2 + Side 3

Example:

Perimeter = AB + BC + CA

               = 10 cm + 15 cm + 10 cm

               = 35 cm

Equilateral Triangle - A triangle whose all sides are of equal length and all angle are of equal measurement is known as equilateral triangle.  

Perimeter of Equilateral Triangle

= Side 1 + Side 2 + Side 3

OR

= 3 x length of triangle (as all 3 sides are equal)

Example:

Perimeter = AB + BC + CA

               = 10 cm + 10 cm + 10 cm

               = 30 cm

OR

               = 3 X 10 cm

               = 30 cm

Note: Perimeter of any rectilinear figure (figure bounded by straight lines) is the sum of the measurement of all sides.

Example:

Perimeter of the above figure 

= AB + BC + CD + DE + EA

= 12 cm + 5 cm + 5 cm + 12 cm + 10 cm

= 44 cm