Introduction to 2D Geometric Shapes

Overview

This lecture explains 2D geometric shapes in detail, their area and perimeter, along with formulas for sectors and segments.

Understanding 2D Shapes

• 2D shapes are those that cannot be held in real life, such as circles, squares, etc.
• 3D shapes can be held, like a cube.
• 2D shapes have only two dimensions (length and width), 3D have three (length, width, height).

Area and Perimeter

• Two things are calculated for 2D shapes: area and perimeter.
• Area = formula must be memorized; perimeter = sum of the lengths of outer edges.
• There is no fixed formula for perimeter, just add all outer boundaries.

Basic Shape Formulas

• Square: Area = L × L = L²; Perimeter = 4L
• Rectangle: Area = L × W; Perimeter = 2L + 2W
• Triangle: Area = ½ × base × height; (also with the help of trigonometry)
• Rhombus/Parallelogram: Area = base × height (height = 90° distance between parallel sides)
• Trapezium: Area = ½ × height × (sum of parallel sides)

Circles and Sectors

• Circle: Area = πr²; Perimeter (circumference) = 2πr
• Sector (pizza slice or pacman):
  • Arc length = θ/360 × 2πr
  • Area = θ/360 × πr²
  • The same angle is used for area in pizza slice and triangle; in major segment, both angles differ.

Circle Segments

• If a circle is cut by a straight line (chord), two parts are formed: major segment and minor segment.
• Major segment = pacman + triangle
• Minor segment = pizza slice - triangle

Method to Find Perimeter

• Add only all sides of the outer boundary, do not memorize any formula.
• In sector or segment, add arc length and other straight sides.

Key Terms & Definitions

• Perimeter — total length of the outer boundaries of a shape.
• Area — total surface inside the shape.
• Circumference — outer boundary (perimeter) of a circle.
• Angle — central angle, necessary when finding sectors.
• Arc Length — length of the curved outer line of a circle, calculated as θ/360 × 2πr.

Action Items / Next Steps

• The lecture on 3D shapes will be covered in the next class.
• Review the triangle area part from the trigonometry marathon video.
• Practice questions on sectors and segments from past papers.