CALCULATING THE AREA OF 2 DIMENSIONAL SHAPES
PART FIVE - A Strategy for Complex Shapes
NCTM Principles and Standards - Ref Pages 243, 244 (Measurement - Grades 6 to 8)

CONCEPT - Disassembly and reassembly
We are going to apply the knowledge of the formula for calculating the area of squares and triangles, to calculate the areas of more complex geometric shapes The concept is 'disassembly and reassembly', which simply means splitting a complex shape down into a number of simple shapes that are easy to measure, and then adding the individual measurements together, to get the total measurement of the complex shape.

CONSTRUCTION (Work In Pairs)
Create the following shapes -

1. One square using 4 squares and one triangle using 4 triangles Combine the shapes - see Fig 1

2. One hexagon using 6 triangles, three rhombus using 2 triangles for each and three parallelograms using 4 triangles for each Combine the shapes - see Fig 2

3. Two rectangles using 3 squares for each, and one trapezoid using 5 triangles Combine the shapes - see Fig 3

Fig 2	Fig 1	Fig 3

4. Calculate the area of each of these 3 complex shapes by visually using the strategy of disassembly and reassembly. Assume the length of a square is 5 inches and the height of a triangle is 4 inches

• Lesson 1
  Study and Definition of 2 Dimensional Shapes
• Lesson 2
  Study and Definition of 3 Dimensional Shapes
• Lesson 3
  Dimensional Nets for 3 Dimensional Solids
• Lesson 4
  Calculating the Area of 2 Dimensional Shapes
• Lesson 5
  Studying the Relationships between Area and Perimeter

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