Calculating Area of Rectangles — Solutions

1. Selecting the Right Unit

   1. Rugby oval: m² ▶ View Solution
   2. Smartphone screen: cm² ▶ View Solution
   3. Queensland: km² ▶ View Solution
   4. Butterfly wing: mm² ▶ View Solution
   5. 1 m² in cm²: 10 000 cm² ▶ View Solution

2. Basic Area Calculation

   1. 12 × 4: 48 cm² ▶ View Solution
   2. 9 × 7: 63 m² ▶ View Solution
   3. 15 × 2: 30 mm² ▶ View Solution
   4. 8 × 8: 64 cm² ▶ View Solution
   5. 25 × 3: 75 m² ▶ View Solution

3. Area of Squares

   1. Side = 5 cm: 25 cm² ▶ View Solution
   2. Side = 11 m: 121 m² ▶ View Solution
   3. Side = 20 km: 400 km² ▶ View Solution
   4. Side = 0.5 cm: 0.25 cm² ▶ View Solution
   5. Area = 144 cm²; side: 12 cm ▶ View Solution

4. Working with Decimals

   1. 6.4 × 3: 19.2 m² ▶ View Solution
   2. 4.5 × 2.2: 9.90 cm² ▶ View Solution
   3. 7.5 × 4: 30 m² ▶ View Solution
   4. 3.2 × 5.5: 17.60 cm² ▶ View Solution
   5. 0.6 × 0.4 in m² and cm²: 0.24 m² (= 2 400 cm²) ▶ View Solution

5. Finding the Missing Dimension

   1. A = 48 cm², w = 6 cm; length: 8 cm ▶ View Solution
   2. A = 100 m², l = 25 m; width: 4 m ▶ View Solution
   3. A = 36 cm² (square); side: 6 cm ▶ View Solution
   4. A = 5.6 m², w = 2 m; length: 2.8 m ▶ View Solution

6. Compound Shape — Additive

   1. Unlabelled dimensions: 8 cm and 4 cm ▶ View Solution
   2. Split into two rectangles: Top (4 × 4 cm) and Bottom (12 × 6 cm) ▶ View Solution
   3. Area of each part: 16 cm² and 72 cm² ▶ View Solution
   4. Total area: 88 cm² ▶ View Solution

7. Compound Shape — Subtractive

   1. Outer rectangle (16 × 10): 160 m² ▶ View Solution
   2. Cut-out area (6 × 4): 24 m² ▶ View Solution
   3. Shaded area: 136 m² ▶ View Solution
   4. New cut-out (12 × 8); remaining area: 64 m² ▶ View Solution

8. Aussie Backyard

   1. Yard area (15 × 8): 120 m² ▶ View Solution
   2. Paved area (3 × 4): 12 m² ▶ View Solution
   3. Turf area: 108 m² ▶ View Solution
   4. Cost at $12/m²: $1 296 ▶ View Solution

9. Error Analysis

   1. What did Henry calculate instead of area? The perimeter (P = 26 cm), not the area ▶ View Solution
   2. Correct area (5 × 8): 40 cm² ▶ View Solution
   3. Was 26 the correct answer to a different question? Yes — 26 cm is the correct perimeter ▶ View Solution

10. The Variable Rectangle

    1. A = 70 cm², l = 10 cm; width: 7 cm ▶ View Solution
    2. Double the width; new area: 140 cm² — doubling one side doubles the area ▶ View Solution
    3. New width = 5 cm; new length and perimeter (vs original): Length = 14 cm; Perimeter = 38 cm (original was 34 cm) ▶ View Solution