Learning Objectives
- Understand the difference between area and perimeter
- Calculate the area of rectangles and squares using formulas
- Calculate the perimeter of rectangles and squares
- Explore the relationship between area and perimeter
Key Concepts
Area vs Perimeter
Area is the amount of space inside a shape (measured in square units). Perimeter is the total length of the boundary around a shape (measured in linear units like cm or m). Think of area as the carpet needed to cover a floor, and perimeter as the fencing needed to go around a garden. They measure different things!
Area of a Rectangle
Area of a rectangle = length x breadth. If a room is 5 m long and 4 m wide, its area is 5 x 4 = 20 sq m. This means you would need 20 tiles of 1 sq m each to cover the floor. Area is always measured in square units: sq cm, sq m, or sq km.
Area of a Square
Area of a square = side x side. If a square garden has sides of 6 m, its area is 6 x 6 = 36 sq m. Since all sides of a square are equal, you only need to know one side length to find the area.
Same Perimeter, Different Area
Two shapes can have the same perimeter but different areas! A rectangle of 1 x 9 has perimeter = 20 and area = 9. A rectangle of 4 x 6 has perimeter = 20 and area = 24. Both have the same perimeter (20 units) but the second has a much bigger area. A square always gives the largest area for a given perimeter.
Important Terms
- Area: The space inside a shape, measured in square units
- Perimeter: The total length around a shape, measured in linear units
- Length: The longer side of a rectangle
- Breadth: The shorter side of a rectangle (also called width)
- Square Units: Units used to measure area (sq cm, sq m)
Quick Revision
- Area of rectangle = length x breadth
- Area of square = side x side
- Perimeter of rectangle = 2 x (length + breadth)
- Perimeter of square = 4 x side
- Same perimeter does not mean same area
- Area is in square units; perimeter is in linear units