Learning Objectives
- Understand the concept of perimeter and area
- Calculate perimeter of rectangles, squares, and triangles
- Calculate area of rectangles and squares
- Estimate area of irregular shapes using squared paper
Key Concepts
Perimeter
The perimeter of a closed figure is the total distance around its boundary. It is the sum of the lengths of all its sides. To find the perimeter, simply add up all the sides of the shape.
Perimeter of a Rectangle: P = 2 × (length + breadth) = 2(l + b)
Perimeter of a Square: P = 4 × side = 4s
Perimeter of a Triangle: P = sum of all three sides = a + b + c
Perimeter of an Equilateral Triangle: P = 3 × side = 3s
Area
The area of a closed figure is the amount of surface it covers. It is measured in square units (e.g., cm², m²). Think of area as the number of unit squares needed to cover a shape completely.
Area of a Rectangle: A = length × breadth = l × b
Area of a Square: A = side × side = s²
Estimating Area of Irregular Shapes
To find the area of an irregular shape, place it on squared paper (graph paper). Count the full squares inside the shape. For squares that are more than half inside, count them as 1. For squares that are less than half inside, ignore them. For squares that are exactly half inside, count them as 1/2. Add them all up to estimate the total area.
Units of Measurement
Perimeter is measured in units of length (cm, m, km). Area is measured in square units (cm², m², km²). Remember: 1 m = 100 cm, so 1 m² = 10,000 cm².
Summary
Mensuration deals with measurement of lengths, perimeters, and areas. Perimeter is the total length of the boundary, while area is the measure of the surface enclosed. Rectangles and squares have simple formulas for both perimeter and area. Irregular shapes can have their area estimated using graph paper.
Important Terms
- Perimeter: The total distance around the boundary of a closed figure
- Area: The amount of surface enclosed within a closed figure
- Square Units: Units used to measure area (cm², m², km²)
- Irregular Shape: A shape that does not have a standard geometric form
Quick Revision
- Perimeter of rectangle = 2(l + b); Area of rectangle = l × b
- Perimeter of square = 4s; Area of square = s²
- Perimeter is measured in cm, m; Area is measured in cm², m²
- Two shapes can have the same perimeter but different areas
- Two shapes can have the same area but different perimeters
- For irregular shapes, use graph paper to estimate area
- A square with side 1 cm has area 1 cm² and perimeter 4 cm