Perimeter

Perimeter

  • Perimeter is the total length or total distance covered along the boundary of a closed shape.
  • Perimeter of a circle is also called as the circumference of the circle.

Example: Find the Perimeter of the given figure.

Solution

Perimeter = Sum of all the sides

= (12 + 3 + 7 + 6 + 10 + 3 + 15 + 12) m

= 68 m

Perimeter of a Triangle

  • Perimeter of triangle = Sum of lengths of all sides  = {\rm{ a }} + {\rm{ b }} + {\rm{ c}}
  • If the given triangle is equilateral that is if all the sides are equal

(a = b = c), then its perimeter is equal to 3 × length of one side of the triangle.

Example

Find the perimeter of a triangle having each side length 13 cm.

Solution

Perimeter of an equilateral triangle = 3 × length of a side

Perimeter of triangle  = {\rm{ }}3{\rm{ }} \times {\rm{ }}13

= 39 cm

Perimeter of a Rectangle

  • Perimeter of the rectangle = length ( l ) + length ( l ) + width (w) + width (w) = 2× [length ( l ) + width (w)]

Example:

The length and breadth of a rectangular swimming pool are 16 and 12 meters respectively. find the perimeter of the pool.

Solution: 

Perimeter of a rectangle = 2 × (length + breadth)

Perimeter of the pool = 2 × (16 + 12)

= 2 × 28 = 56 meters

Perimeter of a Square

Perimeter of square = 4 × length of a side = 4a

Example

Find the perimeter of a square having side length 25 cm.

Solution

Perimeter of a square = 4 × length of a side

Perimeter of square = 4 × 25 = 100 cm

Perimeter of a ‘n’ sided polygon

  • A polygon is a closed shape made up of line segments.
  • Perimeter of n sided polygon = n × length of one side.
  •  Length of each side of a hexagon is a cm, then:
    Perimeter of the hexagon = 6a cm

Example

Find the perimeter of a pentagon having side length 9 cm.

Solution

Perimeter of a regular pentagon = 5 × length of one side

Perimeter of a regular pentagon = 5 × 9

= 45 cm

Perimeter of irregular shapes

  • Irregular shapes are the shapes which do not have all sides and angles equal.
  • The perimeter of irregular shapes is equal to total length covered by the shape.
    In the figure given below, perimeter is the sum of all sides.
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