Fields and Fences

'A farmer needs to know the boundary of his field to build a fence. That boundary is the PERIMETER.'

1. What You Will Learn

• Understanding perimeter — the distance around a shape
• Calculating perimeter of rectangles and squares
• Perimeter of irregular shapes
• Area — the space inside a shape
• Measuring area by counting squares
• Solving word problems about fields and fences

2. What is Perimeter?

Perimeter is the TOTAL DISTANCE around the outside of a shape.

Imagine walking AROUND a field. The distance you walk is the PERIMETER.

Perimeter in Real Life

• Fencing a garden — you need the perimeter
• Putting a frame around a photo — you need the perimeter
• Laying tiles along the edge of a floor — you need the perimeter
• Running around a playground — you run the perimeter

3. Perimeter of a Rectangle

A rectangle has FOUR sides. Opposite sides are EQUAL.

Formula

Perimeter = Length + Width + Length + Width

Or: Perimeter = 2 × (Length + Width)

Example

A rectangular field has length = 20 m and width = 10 m.

Perimeter = 20 + 10 + 20 + 10 = 60 m

Or: 2 × (20 + 10) = 2 × 30 = 60 m

Practice

4. Perimeter of a Square

A square has ALL FOUR sides EQUAL.

Formula

Perimeter = 4 × Side

Example

A square field has side = 15 m.

Perimeter = 4 × 15 = 60 m

5. Perimeter of Irregular Shapes

Not all fields are perfect rectangles! Some have IRREGULAR shapes.

Finding Perimeter of Any Shape

Simply ADD the length of EVERY side.

Example

A field has sides: 10 m, 8 m, 12 m, 6 m, 5 m

Perimeter = 10 + 8 + 12 + 6 + 5 = 41 m

6. What is Area?

Area is the SPACE INSIDE a shape. It tells us how BIG a surface is.

Comparing Area

• Which is bigger — a postcard or a table top? (The TABLE TOP has a larger area)
• Which has more area — a sheet of paper or a page of your notebook? (The NOTEBOOK page has more area)

7. Measuring Area by Counting Squares

How to Measure Area

1. Draw the shape on a grid (each square = 1 unit)
2. Count the FULL squares inside the shape
3. Count the HALF squares (two halves = 1 full square)
4. Add them up — that is the AREA

Example

A rectangle that is 4 squares LONG and 3 squares WIDE:

• Number of squares = 4 × 3 = 12 square units

Area of a Rectangle

Area = Length × Width

Example

A field is 20 m long and 15 m wide. Area = 20 × 15 = 300 square metres (sq m)

8. Word Problems

Problem 1

A farmer has a rectangular field of length 50 m and width 30 m. He wants to put a fence around it. How much fencing does he need? Answer: Perimeter = 2 × (50 + 30) = 2 × 80 = 160 m

Problem 2

A square garden has side 12 m. Find the area. Answer: Area = 12 × 12 = 144 sq m

Problem 3

A field has sides 15 m, 20 m, 15 m, and 20 m. What is the perimeter? Answer: 15 + 20 + 15 + 20 = 70 m

Problem 4

A rectangular park is 40 m long and 25 m wide. Find its area. Answer: Area = 40 × 25 = 1000 sq m

9. Key Facts

• PERIMETER is the DISTANCE AROUND a shape
• AREA is the SPACE INSIDE a shape
• Perimeter uses LINEAR units (m, cm)
• Area uses SQUARE units (sq m, sq cm)
• Same shape, different sizes — BIGGER side length means BIGGER perimeter AND area
• Different shapes can have the SAME perimeter but DIFFERENT areas

10. Common Mistakes

'Do NOT mix up perimeter and area. Perimeter is the BOUNDARY, area is the INSIDE.' 'Do NOT forget to write the UNIT. Perimeter uses m or cm. Area uses sq m or sq cm.' 'Do NOT count only two sides of a rectangle — all FOUR sides make the perimeter.' 'Do NOT use the formula for the wrong shape — a square and a rectangle have different formulas for perimeter.' 'Do NOT forget to ADD all sides for irregular shapes.'

11. Fun Activity

Measure Your Classroom

• Measure the length and width of your classroom (in metres)
• Calculate the perimeter (how much wall you would need to paint a border)
• Calculate the area (how many carpet squares would cover the floor)

Trace and Count

• Draw your hand on a grid paper
• Count the squares inside the outline
• That is the APPROXIMATE area of your hand

Fence Your Garden

• Draw a rectangular garden of your dream size
• Calculate how much fencing you need (perimeter)
• Calculate how many plants can grow (area — one plant per sq m)

12. Self-Test

Q1. Find the perimeter of a rectangle with length 15 m and width 10 m. Answer: 2 × (15 + 10) = 2 × 25 = 50 m

Q2. A square has side 9 m. What is its area? Answer: 9 × 9 = 81 sq m

Q3. An irregular field has sides: 8 m, 6 m, 10 m, 5 m, 7 m. What is the perimeter? Answer: 8 + 6 + 10 + 5 + 7 = 36 m

Q4. A rectangle has length 12 cm and width 8 cm. Find both perimeter and area. Answer: Perimeter = 2 × (12 + 8) = 40 cm. Area = 12 × 8 = 96 sq cm.

Q5. What unit do we use for area? Answer: Square units (sq m, sq cm, sq km)

Q6. If a square has perimeter 40 m, what is the length of ONE side? Answer: 40 ÷ 4 = 10 m

13. Key Vocabulary