Fields and Fences: Class 4 Maths Chapter 13

What is a Boundary? (The 'Fence')

Imagine you have a drawing of a house on a piece of paper. If you trace your finger all the way around the outside edges of the drawing without lifting it, you have just traced its boundary! The boundary is the total length of the line that encloses a shape. In our chapter title, 'Fences' is the word we use for the boundary of a 'Field'. To find the length of the boundary of any shape with straight sides (like a square, rectangle, or triangle), all you have to do is add up the lengths of all its sides. For example, if a farmer's field has four sides, the length of the fence needed would be the sum of the lengths of those four sides. This total length is also called the Perimeter.

How to Calculate the Boundary (Perimeter)

1. Step 1: Look at the Shape — First, carefully observe the field or shape. Note down the length of every single side. Don't miss any!
2. Step 2: Write Down All the Lengths — List all the side lengths you have. For a triangle, you'll have 3 lengths. For a rectangle or square, you'll have 4 lengths.
3. Step 3: Add All the Side Lengths Together — Carefully add up all the numbers you wrote down. The total sum is your answer.
4. Step 4: Write the Final Answer with Units — This is very important! Your final answer must include the unit of measurement, like metres (m) or centimetres (cm). For example, '20 metres'.

Worked Examples: Finding the Boundary

• Example 1: A Rectangular Field
  Rehmat has a rectangular field. Its sides are 10 metres, 20 metres, 10 metres, and 20 metres. What is the length of the boundary?
  Solution:
  To find the boundary, we add the lengths of all four sides.
  Boundary = 10 m + 20 m + 10 m + 20 m
  Boundary = 60 metres.
  So, Rehmat needs 60 metres of wire to fence his field.

• Example 2: A Square Park
  A square park has one side of 15 metres. Since all sides of a square are equal, what is the total length of its boundary?
  Solution:
  A square has 4 equal sides. The length of all sides will be 15 m.
  Total Boundary = 15 m + 15 m + 15 m + 15 m
  Alternatively, Boundary = 4 × length of one side = 4 × 15 m = 60 metres.
  The boundary of the park is 60 metres.

• Example 3: An Irregular Shaped Field
  Ganpat has a field with sides of 9 m, 15 m, 21 m, and 12 m. How much wire does he need for fencing?
  Solution:
  To find the length of the fence, we need to find the total length of the boundary.
  Boundary = 9 m + 15 m + 21 m + 12 m
  Boundary = 57 metres.
  Ganpat needs 57 metres of wire.

Quick Tips for Squares and Rectangles

• For a Square: Since all 4 sides are equal, you can find the boundary by multiplying the length of one side by 4. (Boundary = 4 × Side)
• For a Rectangle: Opposite sides are equal (2 long sides and 2 short sides). You can find the boundary by adding the length and breadth, and then multiplying the sum by 2. (Boundary = 2 × (Length + Breadth))
• Always check the units! If one side is in metres and another in centimetres, you must first change them to the same unit before adding them.

Practice Questions with Solutions

• Q: Rahmat has a square field with each side measuring 30 metres. He wants to put a fence around it. What is the total length of the fence needed?
  A: Step 1: Identify the shape and side length. The field is a square, and each side is 30 metres long.
  Step 2: A square has 4 equal sides. To find the total boundary, we add the length of all four sides: 30 m + 30 m + 30 m + 30 m.
  Step 3: Calculate the sum. 30 + 30 + 30 + 30 = 120 metres. Or, using the shortcut: Boundary = 4 × side = 4 × 30 m = 120 m.
  Final answer: The total length of the fence needed is 120 metres.

• Q: A rectangular table top is 2 metres long and 1 metre wide. What is the perimeter of the table top?
  A: Step 1: Identify the shape and its dimensions. The shape is a rectangle with length = 2 m and width = 1 m.
  Step 2: The sides of the rectangle are 2 m, 1 m, 2 m, and 1 m. To find the perimeter, we add all the side lengths: 2 m + 1 m + 2 m + 1 m.
  Step 3: Calculate the sum. 2 + 1 + 2 + 1 = 6 metres. Or, using the shortcut: Perimeter = 2 × (length + width) = 2 × (2 m + 1 m) = 2 × 3 m = 6 m.
  Final answer: The perimeter of the table top is 6 metres.

• Q: Find the boundary of a field whose sides are 8 m, 10 m, 12 m, and 9 m.
  A: Step 1: The field has four sides with different lengths: 8 m, 10 m, 12 m, and 9 m.
  Step 2: To find the boundary, we must add the lengths of all the sides.
  Step 3: Add the numbers: 8 + 10 + 12 + 9 = 39 metres.
  Final answer: The boundary of the field is 39 metres.

• Q: Chandu's father walks around a park every morning. The park has sides of 100m, 120m, 100m, and 120m. How many metres does he walk in one round?
  A: Step 1: The park is rectangular with two sides of 100m and two sides of 120m.
  Step 2: To find the distance he walks in one round, we need to calculate the boundary (perimeter) of the park.
  Step 3: Add the lengths of all the sides: 100 m + 120 m + 100 m + 120 m.
  Step 4: Calculate the total sum: 100 + 120 + 100 + 120 = 440 metres.
  Final answer: Chandu's father walks 440 metres in one round.

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