Lecture Notes on Area Calculation for Regular Figures

Summary:

In today’s lesson, conducted by Serena, we learned how to calculate the area of regular figures made up of squares and rectangles. The focus was on utilizing units such as square centimeters and square meters. We also explored solving for the area of irregular figures by decomposing them into simpler shapes (squares and rectangles).

Key Concepts and Formulas:

• Area of a Square: ( A = s \times s ) (where ( s ) is the side of the square)
• Area of a Rectangle: ( A = L \times W ) (where ( L ) is the length and ( W ) is the width)

Example Problems:

Problem 1: Calculating Area of a Regular Figure

• Neo and Narlene have a flower garden to calculate the areas.
• Irregular figure solution options:

  1. Solution A (Horizontal Cut):

     • Cut the Garden horizontally to split into a square (X) and a rectangle (Y).
     • Square X: Side = 4 meters, Area = (4m \times 4m = 16m^2)
     • Rectangle Y: Length = 12 meters, Width = 3 meters, Area = (12m \times 3m = 36m^2)
     • Total Area: (16 + 36 = 52m^2)

  2. Solution B (Vertical Cuts):

     • Vertical cuts forming three rectangles (X, Y, Z).
     • Rectangle X: (4m \times 3m = 12m^2)
     • Rectangle Y: (7m \times 4m = 28m^2)
     • Rectangle Z: (4m \times 3m = 12m^2)
     • Total Area: (12 + 28 + 12 = 52m^2)

Problem 2: Miscellaneous Examples

• Various figures were cut into simpler shapes to calculate the area:
  • Example 1:
    • Rectangle X: (2m \times 4m = 8m^2)
    • Rectangle Y: (5m \times 3m = 15m^2)
    • Total Area: (8 + 15 = 23m^2)
  • Example 2:
    • Squares Y and Z: (2cm \times 2cm = 4cm^2) each
    • Rectangle X: 12 square centimeters
    • Total Area: (12cm^2 + 4cm^2 + 4cm^2 = 20cm^2)

Exercises:

• Irregular Figures:
  1. Area = 54 square centimeters
  2. Area = 84 square meters

Practice Problems:

• Mr. Delgado’s Front Yard: Area = 60 square meters
• Students were tasked to find the area of various irregular figures and compare the answers with provided solutions.

Conclusion:

By decomposing irregular shapes into known figures such as squares and rectangles, we can effectively calculate the area using fundamental geometric formulas. This method provides an efficient way to deal with complex shapes routinely encountered in real-world applications.

Remember, practice is essential to mastering these techniques, as demonstrated in today’s session. Please use these notes to help understand the fundamental concepts and practice with additional problems.