Irregular Shape Area Decomposition

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Irregular shapes decomposed into rectangles and triangles

🏠 Part 1: Breaking Down Shapes

1. You need to buy carpet for an L-shaped room. Which shapes would you break it into?

Two rectangles

One triangle and one circle

Three squares

One rectangle and one triangle

2. To find the area of a triangle, you use:

length × width

½ × base × height

base + height

2 × base × height

3. Look at the irregular shape below (drawn on grid paper). Draw lines to break it into rectangles and triangles.

4. Which of these are good strategies for decomposing irregular shapes? (Tick all that apply)

Look for rectangular sections first

Draw straight lines to create familiar shapes

Always start with triangles

Make sure shapes don't overlap when adding areas

📐 Part 2: Calculate the Areas

5. A rectangle has length 6 cm and width 4 cm. Its area is _______ cm².

6. A triangle has base 8 cm and height 5 cm. Its area is _______ cm².

7. An irregular shape is made of:

• Rectangle A: 5 cm × 3 cm

• Rectangle B: 4 cm × 2 cm

Show your working to find the total area:

8. A garden patch is shaped like a rectangle with a triangular section added. The rectangle is 10 metres × 6 metres. The triangle has base 6 metres and height 4 metres. What is the total area?

🎯 Part 3: Problem Solving

9. Draw an irregular shape on the grid below and decompose it into at least 2 different shapes. Label the dimensions and calculate the total area.

My total area calculation:

10. Explain in your own words: Why is it helpful to break irregular shapes into rectangles and triangles?

11. Extension Challenge: A room has an area of 48 m². It's made of two rectangles. One rectangle is 6 m × 4 m. What could the dimensions of the second rectangle be?