Learning Objectives
- Understand the concept of perimeter
- Calculate the perimeter of simple shapes
- Learn the relationship between perimeter and fencing
- Solve real-life problems involving perimeter
Key Concepts
What is Perimeter?
Perimeter is the total length of the boundary of a shape. If you walk along the edges of a playground and come back to where you started, the total distance you walked is the perimeter. Perimeter is measured in cm, m, or km. To find the perimeter, add up the lengths of all the sides.
Perimeter of a Rectangle
A rectangle has 4 sides. The two longer sides are called the length, and the two shorter sides are called the breadth (or width). Perimeter of a rectangle = length + breadth + length + breadth = 2 x (length + breadth). If a garden is 10 m long and 6 m wide, its perimeter is 2 x (10 + 6) = 2 x 16 = 32 m.
Perimeter of a Square
A square has 4 equal sides. Perimeter of a square = 4 x side. If each side of a square playground is 20 m, its perimeter is 4 x 20 = 80 m. This is the total length of fencing needed to go around the playground.
Fencing a Field
If a farmer wants to put a fence around a rectangular field that is 50 m long and 30 m wide, the total fencing needed is the perimeter = 2 x (50 + 30) = 160 m. If fencing wire costs Rs 15 per metre, the total cost is 160 x 15 = Rs 2400. Perimeter helps us plan fencing, borders, and frames.
Important Terms
- Perimeter: The total distance around a shape
- Boundary: The edge or border of a shape
- Length: The longer side of a rectangle
- Breadth (Width): The shorter side of a rectangle
- Fencing: A wire or material used to go around a field or garden
Quick Revision
- Perimeter = sum of all sides
- Perimeter of rectangle = 2 x (length + breadth)
- Perimeter of square = 4 x side
- Perimeter tells us how much fencing is needed
- Total cost of fencing = perimeter x cost per metre
- Perimeter is measured in cm, m, or km