Perimeter of Various Shapes for Class 4

Perimeter is an important concept that helps us understand the measurement of the boundary of a shape or object. In this chapter, we will explore the concept of perimeter of different shapes.

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 determined by adding the length of all the sides enclosing the shape.

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 cm, 7 cm and 6 cm?

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

Answer: c) 21 cm

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

So, the perimeter of this triangle is 21 cm.

Perimeter of a Square

A square is a special shape with four equal sides.

We have a formula for determining the square's perimeter. Let's explore to see the derivation of the formula.

Perimeter of the square ABCD = Sum of all sides of a square
                                               = a + a + a + a
                                               = 4 × a
Where a: length of each side of a square.

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

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

Answer: b) 48 m

Explanation: We know that perimeter of a square = 4 x length of a side

Perimeter of a square field = 4 × 12 = 48 m

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

Perimeter of Rectangle

A rectangle has two pairs of equal sides. 

Let's see how can we find the perimeter of a rectangle:

Perimeter of the rectangle = l + b + l + b
                                          = 2 × (l + b) 
Where l: length of a rectangle
          b: breadth/width of a rectangle

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

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

Answer: d) 86 m

Explanation: 

Perimeter of a rectangular garden = 2 (l + b) 
                                                 = 2 (25 + 18)
                                                 = 2 × 43
                                                 = 86 m

The perimeter of this rectangular garden is 86 m.