Area and Perimeter of Quadrilaterals — Solutions

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1. Perimeter of quadrilaterals Fluency

   1. 26 cm
   2. 44 m
   3. 41 cm
   4. 9.6 m
   5. 34 cm
   6. 10.6 m
   7. 34 mm
   8. 42 m

2. Area of rectangles and squares Fluency

   1. 36 cm²
   2. 49 m²
   3. 100 cm²
   4. 2.25 km²
   5. 720 mm²
   6. 125.44 m²
   7. 22.4 m²
   8. 0.81 cm²

3. Area of parallelograms Fluency

   1. 40 cm²
   2. 126 m²
   3. 26 cm²
   4. 260 mm²
   5. 82.5 m²
   6. 83 200 cm²  (3.2 m × 2.6 m = 8.32 m² = 83 200 cm²)
   7. 450 cm²
   8. 30.8 m²

4. Find missing dimensions Understanding

   1. Width = 8 cm  (72 ÷ 9)
   2. Side = 12 m  (√144)
   3. Width = 7 cm  (38 − 2×12 = 14; 14÷2)
   4. Height = 6 cm  (90 ÷ 15)
   5. Side = 13 m; Area = 169 m²
   6. Width = 5.75 m, Length = 17.25 m  (2(w + 3w) = 46; 8w = 46)
   7. Base = 8 m  (48 ÷ 6)
   8. Side = 16 cm; Perimeter = 64 cm

5. Composite shapes — area Understanding

   1. 68 cm²  (80 − 12)
   2. 63 cm²  (12×3 + 3×12 − 3×3 overlap = 36 + 36 − 9)
   3. 58 m²  (40 + 18)
   4. 88 cm²  (56 + 32)
   5. 126 m²  (150 − 24)
   6. 18 cm²  (3 steps × 3 cm × 2 cm)

6. Problem Solving Problem Solving

   1. 1. 17.28 m²  (4.8 × 3.6)
      2. $483.84  (17.28 × $28)
      3. 19.008 m²  (17.28 × 1.1); buy 19.1 m² (round up)
   2. 1. 410 m  (2 × (120 + 85))
      2. $7585  (410 × $18.50)
      3. 147.0 m  (√(14 400 + 7 225) = √21 625 ≈ 147.0 m)
   3. 1. 20.8 m²  (6.5 × 3.2)
      2. 11 bags  (20.8 ÷ 2 = 10.4, round up to 11)
      3. $98.89  (11 × $8.99)

7. Area and perimeter from diagrams Understanding

   1. Area = 44 cm²; Perimeter = 30 cm
   2. Area = 36 m²; Perimeter = 24 m
   3. Area = 105 cm²  (15 × 7)

8. Formula reference table Understanding

   1. Area = 45 cm²; Perimeter = 28 cm
   2. Area = 64 m²; Perimeter = 32 m
   3. Area = 84 cm²; Perimeter = 42 cm
   4. Area = 260 mm²; Perimeter = 66 mm
   5. Area = 20.25 km²; Perimeter = 18 km
   6. Area = 48 m²; Perimeter = 30 m

9. Spot the error Understanding

   1. Sam used slant side (5 cm) instead of perpendicular height (4 cm). Correct: A = 8 × 4 = 32 cm²
   2. Jordan multiplied instead of using P = 2(l + w). Correct: P = 2(7 + 3) = 20 cm
   3. Alex calculated the perimeter, not the area. Correct: A = 5² = 25 m²
   4. Riley used P² instead of s². Side = 24 ÷ 4 = 6 cm; Correct: A = 6² = 36 cm²

10. Design a room Problem Solving

    1. Bedroom: 15.12 m²; Lounge: 31.2 m²; Kitchen: 11.4 m²
    2. 57.72 m²
    3. Carpet: 15.12 × $42 = $635.04; Vinyl: 42.6 × $19 = $809.40; Total: $1444.44
    4. Bedroom: 15.6 m; Lounge: 22.6 m; Kitchen: 13.6 m; Total: 51.8 m
    5. 51.8 × $4.80 = $248.64