Finding the Area of Composite Shapes

Introduction

Topic: Finding areas of complex shapes by decomposing them into simpler shapes.
Challenge: Strange shapes don't have predefined area formulas like rectangles or triangles.
Solution: Break complex shapes into simple shapes with known formulas.

Composite Shapes: Made of two or more simple shapes.
Strategy: Split the shape into rectangles, triangles, and/or trapeziums and calculate each area separately.

Shape Description: Top part is a triangle, bottom part is a rectangle.
Steps:
1. Rectangle Area:
  - Formula Used: Length x Width
  - Calculation: 5cm x 4cm = 20cm²
2. Triangle Area:
  - Formula Used: 1/2 x Base x Height
  - Given: Base = 5cm, Height needs calculation
  - Height Calculation: Overall height = 7cm, Rectangle height = 4cm
  - Height of Triangle: 7cm - 4cm = 3cm
  - Area Calculation: 1/2 x 5cm x 3cm = 7.5cm²
3. Total Area: 20cm² + 7.5cm² = 27.5cm²

Shape Description: Bottom is a rectangle, top is a trapezium.
Steps:
1. Rectangle Area:
  - Formula Used: Length x Width
  - Calculation: 15cm x 12cm = 180cm²
2. Trapezium Area:
  - Formula Used: (a + b)/2 x Height
  - Given: Top length (a) = 4cm, Bottom length (b) = 6cm, Height = 5cm
  - Average Length Calculation: (4cm + 6cm)/2 = 5cm
  - Area Calculation: 5cm x 5cm = 25cm²
3. Total Area: 180cm² + 25cm² = 205cm²

Composite shapes can be broken down into simple shapes with known area formulas.
Calculation involves finding and summing the areas of each simple shape.