Practice Maths

Topic Review — Area and Perimeter

Mixed Practice — L24 – L27

This review covers all lessons in the Area and Perimeter topic. Try each question before checking your answers.

Review Questions

  1. Area unit conversion. Fluency

    1. Convert 6.5 m² to cm².
    2. Convert 480 mm² to cm².
    3. Convert 3 ha to m².
    4. Convert 250 000 m² to km².
    5. Convert 0.8 km² to ha.
    6. A rectangular wall panel is 240 cm × 180 cm. Find its area in m².

  2. Area and perimeter of standard quadrilaterals. Fluency

    1. Find the area and perimeter of a rectangle 13 cm × 7 cm.
    2. Find the area and perimeter of a square with side 9.5 m.
    3. A parallelogram has base 11 m, perpendicular height 8 m, and slant side 9 m. Find its area and perimeter.
    4. A rectangle has area 84 cm² and width 6 cm. Find its length and perimeter.
    5. A square has perimeter 64 m. Find its area.

  3. Area of rhombuses, kites and trapeziums. Understanding

    1. Find the area of a rhombus with diagonals 16 cm and 10 cm.
    2. Find the area of a kite with diagonals 9 m and 6 m.
    3. Find the area of a trapezium with parallel sides 14 cm and 8 cm, and height 7 cm.
    4. A rhombus has area 60 cm² and one diagonal of 15 cm. Find the other diagonal.
    5. A trapezium has area 75 m² and height 6 m. One parallel side is 9 m. Find the other.
    6. A kite has diagonals in the ratio 2 : 3. The shorter diagonal is 8 cm. Find the area.

  4. Composite shapes — area and perimeter. Understanding

    1. An L-shaped room has outer dimensions 11 m × 9 m with a 4 m × 3 m notch removed from one corner. Find the area.
    2. A composite shape consists of a rectangle 10 cm × 6 cm with a triangle on top (base 10 cm, height 4 cm). Find the total area.
    3. A large rectangle 20 cm × 12 cm has a small rectangle 8 cm × 5 cm removed from the inside. Find the shaded area.
    4. Find the perimeter of an L-shape with outer dimensions 14 m × 10 m and a rectangular notch 6 m × 4 m removed from one corner.
    5. A composite shape has a rectangle 8 m × 5 m with a trapezium attached to one long side. The trapezium has parallel sides 8 m and 5 m, and height 3 m. Find the total area.

  5. Real-world problem solving. Problem Solving

    1. A house block is 32 m × 24 m. The house footprint on the block is a rectangle 18 m × 12 m.
      1. Find the total block area in m².
      2. Find the garden area (block minus house).
      3. Lawn fertiliser covers 50 m² per bag and costs $14.50 per bag. How much does it cost to fertilise the entire garden?
    2. A swimming pool area (top view) is L-shaped: the main pool is 12 m × 5 m and the shallow end extension is 4 m × 3 m.
      1. Find the total pool surface area.
      2. Pool tiles cost $65 per m². Find the tiling cost.
      3. A safety fence runs around the full perimeter of the pool. Find the minimum length of fencing needed.
    3. A block of land is trapezium-shaped with parallel sides of 60 m and 45 m and a perpendicular distance of 40 m between them.
      1. Calculate the area of the block in m².
      2. Convert to hectares.
      3. A fence runs along all four sides. If the two non-parallel sides are 42 m and 38 m respectively, find the total perimeter.
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