Math with Mr. Jay: Finding Area

Overview

• Objective: Learn how to find the area of rectangles, squares, triangles, and circles.
• Definition: Area is the amount of surface a shape covers, measured in square units.

Rectangles

• Formula: Area = Length × Width
• Example 1:
  • Length = 6 meters, Width = 3 meters
  • Area = 6 × 3 = 18 square meters
  • Visualization: Draw squares to represent square meters.
• Example 2:
  • Length = 19 feet, Width = 5 feet
  • Area = 19 × 5 = 95 square feet
  • Note: Only need length and width, even if all sides are given.

Squares

• Formula: Area = Side length²
• Example 1:
  • Side = 8 inches
  • Area = 8² = 64 square inches
• Example 2:
  • Side = 11 meters
  • Area = 11² = 121 square meters
  • Symbols: Tick marks and 90-degree angles show equal sides.

Triangles

• Formulas:
  • Area = (Base × Height) / 2
  • Or Area = 1/2 × Base × Height
• Example 1:
  • Base = 8 feet, Height = 6 feet
  • Area = (8 × 6) / 2 = 24 square feet
  • Explanation: Two triangles form a rectangle; hence, half is used for area.
• Example 2:
  • Base = 9 meters, Height = 4 meters
  • Area = (9 × 4) / 2 = 18 square meters
• Example 3:
  • Base = 5 yards, Height = 11 yards
  • Area = (5 × 11) / 2 = 27.5 square yards
  • Visualization: Copy triangle to form a parallelogram.

Circles

• Formula: Area = πr² (π times radius squared)
• Concepts:
  • Diameter: Distance across the circle through the center.
  • Radius: Half of the diameter.
  • Pi (π): Ratio of circumference to diameter, approximately 3.14.
• Example 1 (Radius Given):
  • Radius = 9 cm
  • Area = π × 9² = 81π square cm
  • Approximate: 3.14 × 81 = 254.34 square cm
• Example 2 (Diameter Given):
  • Diameter = 12 feet
  • Radius = 12 / 2 = 6 feet
  • Area = π × 6² = 36π square feet
  • Approximate: 3.14 × 36 = 113.04 square feet

Conclusion

• Covered techniques to calculate areas of key geometric shapes.
• Used visual aids and formulae to reinforce understanding.