Area Units and Conversion — Solutions

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1. Convert between mm² and cm² Fluency

   1. 400 mm²
   2. 7 cm²
   3. 1250 mm²
   4. 3.5 cm²
   5. 80 mm²
   6. 25 cm²
   7. 900 mm²
   8. 0.48 cm²

2. Convert between cm² and m² Fluency

   1. 20 000 cm²
   2. 5 m²
   3. 7 500 cm²
   4. 0.84 m²
   5. 35 000 cm²
   6. 12.5 m²
   7. 400 cm²
   8. 0.096 m²

3. Convert between ha, m² and km² Fluency

   1. 30 000 m²
   2. 25 ha
   3. 150 ha
   4. 4.5 km²
   5. 6 000 m²
   6. 8 ha
   7. 2 800 000 m²
   8. 5 km²

4. Most appropriate unit Understanding

   1. mm² — very small area
   2. ha or m² — large outdoor space, thousands of m²
   3. km² — enormous area
   4. m² — typical room size
   5. cm² or mm² — small flat object
   6. ha or km² — very large land area
   7. cm² — medium-sized flat object
   8. km² or ha — very large land area

5. Problem Solving Problem Solving

   1. 1. 144 000 cm²  (450 × 320)
      2. 14.4 m²  (144 000 ÷ 10 000)
      3. $648  (14.4 × $45)
   2. 1. 28 km²  (2800 ÷ 100)
      2. 80 paddocks  (2800 ÷ 35)
      3. 112 tonnes  (35 × 3.2)
   3. 1. 400 cm²  (20 × 20)
      2. 40 000 mm²  (400 × 100)
      3. 180 tiles  (7.2 m² = 72 000 cm²; 72 000 ÷ 400 = 180)

6. Order areas from smallest to largest Understanding

   1. 450 mm², 5 cm² = 0.0005 m²
   2. 18 000 m², 2 ha (20 000 m²), 0.025 km² (25 000 m²)
   3. 9 500 cm², 1 m² (10 000 cm²), 0.00012 km² (120 m²)
   4. 0.000028 m² (28 mm²), 2.9 cm² (290 mm²), 300 mm²
   5. 4 800 m², 0.5 ha (5 000 m²), 0.006 km² (6 000 m²)
   6. 95 ha (950 000 m²), 1 km² (1 000 000 m²), 1 100 000 m²

7. True or false Understanding

   1. False — 1 m² = 10 000 cm²
   2. False — multiply by 10 000 (not 100)
   3. True
   4. True — 2.5 × 100 = 250 ha
   5. True — 50 000 ÷ 10 000 = 5 m²
   6. True
   7. True — 1 km² = 100 ha
   8. False — multiply by 100 (not 10)

8. Extended response Problem Solving

   1. 1. 1.6335 m²
      2. 16 335 cm²
      3. 29.403 m²
   2. 1. 348 km²
      2. 3.48 × 10⁸ m²
      3. 0.0034%
   3. 1. Option A: 400 cm² = 0.04 m²; Option B: 1 000 cm² = 0.10 m²
      2. Area with wastage = 9.24 m²; Option A: 24 boxes; Option B: 12 boxes
      3. Option A: $528; Option B: $312 — Option B is cheaper

9. Conversion chain Understanding

   1. 50 000 mm²
   2. 36 000 cm²
   3. 4.5 km²
   4. 2 000 m²
   5. 7.5 m²
   6. 28 cm²

10. Spot the error Problem Solving

    1. Error: multiplied by 100 not 10 000. Correct: 2 m² = 20 000 cm²
    2. Error: divided by 10 instead of multiplying by 10 000. Correct: 5 ha = 50 000 m²
    3. Error: used linear factor 1 000 instead of 1 000². Correct: 1 km² = 1 000 000 m²
    4. Error: divided by 10 instead of 100. Correct: 30 mm² = 0.3 cm²