Shapes and Problem Solving

Name:

Date:

🎯 WALT (We Are Learning To)

• Apply properties of shapes to solve real-world problems

• Use reasoning and estimation skills with geometric measurements

• Calculate areas and perimeters in practical contexts

Success Criteria:

🟢 I can identify and use properties of 2D shapes

🟡 I can calculate areas and perimeters accurately

🔵 I can solve multi-step problems involving shapes

📚 Part 1: Shape Properties & Reasoning

1. A regular octagon has a perimeter of 64 cm. What is the length of each side?

6 cm

8 cm

10 cm

12 cm

2. Which properties apply to a rhombus? (Select all that apply)

All sides are equal

All angles are 90°

Opposite sides are parallel

Diagonals bisect each other at right angles

3. Estimation Challenge: A circular garden has a radius of approximately 4.2 metres. Estimate its area to the nearest 10 square metres.

My estimate: _______ m² Strategy used: _________________________

4. Real-World Application: Sarah is designing a triangular flag with a base of 80 cm and height of 60 cm. She wants to add a gold border around the edges. If gold trim costs $3.50 per metre, estimate the total cost for the border.

✏️ Part 2: Problem Solving & Analysis

5. A rectangular swimming pool is 25 metres long and 12 metres wide. The council requires a 2-metre safety fence around the entire perimeter. Calculate the area that will be enclosed by the fence (including the pool).

6. Reasoning: Explain why the area of a triangle is half the area of a rectangle with the same base and height. Use a diagram to support your explanation.

7. Challenge Problem (Extension): A regular hexagon is inscribed in a circle with radius 10 cm. Calculate the area of the hexagon. (Hint: Divide into triangles)

8. Differentiation - Choose Your Level:

🟢 Foundation: Find the area of a rectangle: length = 15 cm, width = 8 cm

🟡 Standard: Find the area of a parallelogram: base = 12 cm, height = 9 cm

🔵 Advanced: Find the area of a trapezium: parallel sides = 14 cm and 8 cm, height = 6 cm

9. Exit Ticket - Hinge Point Question: If you double the dimensions of a square, how does this affect its area? Explain your reasoning.