Perimeter of Various Shapes

Perimeter is an important concept that helps students understand the measurement of the boundary of a shape or object. In this chapter, we will explore the concept of perimeter and how it prepares students for more advanced mathematical concepts.

Perimeter

Perimeter is defined as the distance around the edge of a two-dimensional shape. It is a fundamental concept in geometry and plays a vital role in solving real-world problems involving measurement.

Perimeter is the length of the boundary or fence of a two-dimensional shape. It is the sum of the lengths of all sides of polygons (any closed figures) such as squares, rectangles, etc.

The units used for the perimeter are metres, centimetres, millimetres, etc.

Perimeter of Triangle

Perimeter of the triangle is the sum of all three sides.

In triangle ABC,

Perimeter of the triangle = a + b + c

Where a, b and c are the sides of a triangle.

Example: What is the perimeter of a triangle with sides measuring 8 centimetres, 7 centimetres and 6 centimetres?

a) 12 cm
b) 15 cm
c) 21 cm
d) 51 cm

Answer: c) 21 cm

Explanation: Perimeter of the triangle = 8 cm + 7 cm + 6 cm = 21 cm

So, the perimeter of this triangle is 21 centimetres.

Perimeter of Square

A square is a special shape with four equal sides.

Perimeter of the square is the sum of all four sides.

In square ABCD,

Perimeter of the square = a + a + a + a
                                   = 4 × a
                                    = 4 × (length of a side)

Where a is the equal sides of a square.

Example: What is the perimeter of a square field with each side measuring 12 metres?

a) 24 m
b) 48 m
c) 72 m
d) 96 m

Answer: b) 48 m

Explanation: A square field with each side measuring 12 metres is shown as:

Perimeter of a square field = 12 m + 12 m + 12 m + 12 m = 48 m

OR

Perimeter of a square field = 4 (length of a side)
                                       = 4 × 12 m
                                        = 48 m

So, the perimeter of this square field is 48 metres.

Perimeter of Rectangle

A rectangle has two pairs of equal sides. 

Perimeter of a rectangle is the sum of all four sides.

In rectangle ABCD, 

Perimeter of the rectangle = l + b + l + b
                                       = 2 × (l + b) 
                                        = 2 (length + breadth)

Where l is the length and b is the breadth/width of a rectangle.

Example: What is the perimeter of a rectangular garden with a length of 25 metres and a breadth of 18 metres?

a) 43 m
b) 56 m
c) 76 m
d) 86 m

Answer: d) 86 m

Explanation: Perimeter of a rectangular garden = 2 (length + breadth) 
                                                                       = 2 (25 + 18)
                                                                        = 2 × (43)
                                                                         = 86 m

OR

Perimeter of a rectangular garden = (l + b) + (l + b)
                                                  = (25 m + 18 m) + (25 m + 18 m) 
                                                   = 43 m + 43 m
                                                    = 86 m

The perimeter of this rectangular garden is 86 metres.