MathIsimple

Lesson 4-2: Area & Perimeter

Calculate area and perimeter of rectangles and other shapes using garden design scenarios!

Learning Scenario: Garden Design

Scenario: You're designing a rectangular vegetable garden for your school. The garden will be 8 meters long and 6 meters wide. You need to know how much soil to buy (area) and how much fencing to put around it (perimeter). Can you help calculate these measurements?

What We Need to Find:

  • • Area: How much space inside the garden
  • • Perimeter: Distance around the garden
  • • Garden dimensions: 8m × 6m
  • • Materials needed for the project

Tools We'll Use:

  • • Area formula: length × width
  • • Perimeter formula: 2 × (length + width)
  • • Multiplication and addition
  • • Real-world problem solving

Understanding Area

What is Area?

Area is the amount of space inside a shape. It tells us how much surface the shape covers. We measure area in square units like square meters (m²), square feet (ft²), or square centimeters (cm²).

Area = Length × Width

For rectangles and squares

Think of Area As:

How many square tiles would fit inside the shape

Real Examples:

Floor space, garden beds, painting walls

Calculating Area

Step-by-Step: Garden Area

Let's calculate the area of our 8m × 6m garden:

Given: Length = 8m, Width = 6m

Our garden dimensions

Area = Length × Width

Formula for rectangle area

Area = 8m × 6m = 48m²

Calculate the area

Answer: 48 square meters

This is how much soil we need!

Understanding Perimeter

What is Perimeter?

Perimeter is the distance around the outside of a shape. It's like walking around the edge of the shape and measuring how far you've traveled. We measure perimeter in regular units like meters (m), feet (ft), or centimeters (cm).

Perimeter = 2 × (Length + Width)

For rectangles and squares

Think of Perimeter As:

How much fence you need to go around the shape

Real Examples:

Fencing, borders, running tracks

Calculating Perimeter

Step-by-Step: Garden Perimeter

Let's calculate the perimeter of our 8m × 6m garden:

Given: Length = 8m, Width = 6m

Our garden dimensions

Perimeter = 2 × (Length + Width)

Formula for rectangle perimeter

Perimeter = 2 × (8m + 6m)

Substitute the values

Perimeter = 2 × 14m = 28m

Calculate step by step

Answer: 28 meters

This is how much fencing we need!

Practice Problems

Problem 1: Classroom Floor

A classroom is 12 meters long and 9 meters wide. Find both the area and perimeter.

Area = 12m × 9m = 108m²

Area calculation

Perimeter = 2 × (12m + 9m) = 2 × 21m = 42m

Perimeter calculation

Answer: Area = 108m², Perimeter = 42m

Problem 2: Square Garden

A square garden has sides of 5 meters each. Find both the area and perimeter.

Area = 5m × 5m = 25m²

For squares: side × side

Perimeter = 4 × 5m = 20m

For squares: 4 × side

Answer: Area = 25m², Perimeter = 20m

Real-World Applications

Where We Use Area & Perimeter

Area Applications

  • • Flooring and carpet installation
  • • Painting walls and ceilings
  • • Garden planning and soil calculation
  • • Land surveying and property measurement

Perimeter Applications

  • • Fencing and border installation
  • • Running tracks and race courses
  • • Picture frames and molding
  • • Security perimeters and boundaries

Key Takeaways

Area

  • •Area = Length × Width (for rectangles)
  • •Measures space inside a shape
  • •Measured in square units (m², ft², cm²)
  • •Used for flooring, painting, gardening

Perimeter

  • •Perimeter = 2 × (Length + Width) (for rectangles)
  • •Measures distance around a shape
  • •Measured in regular units (m, ft, cm)
  • •Used for fencing, borders, tracks
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