The perimeter of a plane shape is the total distance around the boundary of the shape.

For polygons, the perimeter is found by adding the lengths of all the sides.

A regular polygon is a polygon whose sides and angles are all equal.

Example: Square, Equilateral triangle, Regular hexagon, etc.

Square:

• All 4 sides equal.


• Perimeter P = 4s

+------+
|      |
|      |
+------+

(s = side length)

Rectangle:

• Opposite sides equal.


• Perimeter P = 2(l + b)

+----------+
|          |
|          |
+----------+

(l = length, b = breadth)

Triangle:

• If equilateral (regular): P = 3a


• If scalene or isosceles: add all sides.

   /\
  /  \
 /____\

(a = side of equilateral triangle)

Trapezium:

• Perimeter = sum of all 4 sides.


• Only special trapeziums (isosceles) can be considered “regular-like”.

  +------+
 /        \
+----------+

Parallelogram:

• Opposite sides equal.


• Perimeter P = 2(a + b)

  /------/
 /      /
/------/

Circle:

• Circle has no sides, but its “perimeter” is called circumference.


• C = 2πr or C = πd

   ****
 *      *
*        *
 *      *
   ****

WORKED EXAMPLES

Example 1: Square
Find the perimeter of a square with side 12 cm.

Solution:

P = 4s

= 4 × 12

= 48 cm

Answer: 48 cm

Example 2: Rectangle

A rectangle is 15 cm long and 8 cm wide. Find its perimeter.

Solution:

P = 2(l + b)

= 2(15 + 8)

= 2 × 23

= 46 cm

Answer: 46 cm

Example 3: Equilateral Triangle

Each side of an equilateral triangle is 7 cm. Find its perimeter.

Solution:

P = 3a

= 3 × 7

= 21 cm

Answer: 21 cm

Example 4: Trapezium

The sides of a trapezium are 10 cm, 8 cm, 7 cm and 9 cm. Find its perimeter.

Solution:
P = a + b + c + d

= 10 + 8 + 7 + 9

= 34 cm

Answer: 34 cm

Example 5: Parallelogram

A parallelogram has adjacent sides 12 cm and 9 cm. Find its perimeter.

Solution:

P = 2(a + b)

= 2(12 + 9)

= 2 × 21

= 42 cm

Answer: 42 cm

Example 6: Circle (Circumference)

Find the circumference of a circle of radius 14 cm. Use π = 22/7.

Solution:

C = 2πr

= 2 × 22/7 × 14

= 2 × 44

= 88 cm

Answer: 88 cm

SUMMARY

• Perimeter means the distance around a shape.


• For polygons, add up the sides.


• For regular polygons, multiply the number of sides by the side length.


• Circle’s perimeter is called circumference.


• Formulae:


• Square: 4s


• Rectangle: 2(l + b)


• Triangle: 3a (if equilateral)


• Parallelogram: 2(a + b)


• Trapezium: a + b + c + d


• Circle: 2πr or πd