📐 Part 1: Area Formulas and Decomposition

1. What is the formula for the area of a triangle?

Area = base × height

Area = ½ × base × height

Area = 2 × base × height

Area = base + height

2. What is the formula for the area of a parallelogram?

Area = ½ × base × height

Area = base × height

Area = 2 × (base + height)

Area = base ÷ height

3. Which shapes are most useful for decomposing composite shapes? (Select all that apply)

Triangles

Parallelograms

Circles

Rectangles

4. A composite shape is made of a rectangle (8 cm × 5 cm) and a triangle (base 6 cm, height 4 cm). What is the total area?

Total area = _________ cm²

🔍 Part 2: Problem Solving

5. A composite shape consists of a parallelogram with base 10 cm and height 6 cm, plus a triangle with base 4 cm and height 3 cm attached to one side. Calculate the total area.

6. Explain why breaking composite shapes into triangles and parallelograms makes area calculations easier.

7. A garden bed is shaped like a rectangle (12 m × 8 m) with a triangular section (base 6 m, height 4 m) added to one end. What is the total area of the garden bed?

Show your working and include units: _________ m²

8. Design your own composite shape problem:

a) Draw a composite shape made of at least two simple shapes in the box below:

b) Label the dimensions on your shape and write a word problem:

c) Solve your own problem:

🎯 Part 3: Quick Quiz

9. A composite shape has a parallelogram (base 7 cm, height 5 cm) and a triangle (base 8 cm, height 6 cm). What is the total area?

59 cm²

35 cm²

24 cm²

83 cm²

10. What is the first step when finding the area of a composite shape?

11. A sports field consists of a rectangular section (50 m × 30 m) with two triangular end zones (each with base 30 m and height 10 m). Calculate the total area of the field.

Total field area = _________ m²