Measurement applications: compound shapes

Task goals

• Split a compound shape into simpler component shapes, or identify an excluded region to subtract, from a realistic scenario.
• Calculate the total area of a compound shape by adding component areas or subtracting an excluded region.
• Calculate the perimeter of a compound shape using only its true outer boundary, including a curved edge's arc length where present.
• Convert between units of length or area before calculating, and recognise that an area conversion factor is squared.
• Use a calculated area or perimeter to find a quantity of material needed for a real task.
• Calculate the total cost of a quantity of material, rounding a discrete purchase (tins, rolls, sheets, packs, bags) UP to the next whole item and money to the nearest cent.
• Compare two real options by total cost and/or value per unit area, and check whether each meets a stated constraint such as a budget or a free-delivery threshold.
• Write a short, numbers-based justification for a real-world measurement decision.