Let’s solve each problem one by one. We’ll calculate area and perimeter for each quadrilateral using the correct formulas.
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Problem 1: Square (all sides equal, right angles)
Side = 6.6 yd
Area = side × side = 6.6 × 6.6 =
43.56 yd²
Perimeter = 4 × side = 4 × 6.6 =
26.4 yd
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Problem 2: Rectangle
Length = 9.3 in, Width = 3.3 in
Area = length × width = 9.3 × 3.3 = let’s compute:
9 × 3.3 = 29.7, 0.3 × 3.3 = 0.99 → total = 29.7 + 0.99 =
30.69 in²
Perimeter = 2 × (length + width) = 2 × (9.3 + 3.3) = 2 × 12.6 =
25.2 in
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Problem 3: Parallelogram
Base = 16.6 m, Height = 8.8 m, Side = 6.9 m
Area = base × height = 16.6 × 8.8
Let’s break it down:
16 × 8.8 = 140.8
0.6 × 8.8 = 5.28
Total = 140.8 + 5.28 =
146.08 m²
Perimeter = 2 × (base + side) = 2 × (16.6 + 6.9) = 2 × 23.5 =
47.0 m
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Problem 4: Trapezoid
Bases: top = 7 cm, bottom = 18 cm, height = 8 cm, non-parallel sides = 9 cm each
Area = ½ × (sum of bases) × height = ½ × (7 + 18) × 8 = ½ × 25 × 8 = 12.5 × 8 =
100 cm²
Perimeter = sum of all sides = 7 + 18 + 9 + 9 =
43 cm
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Problem 5: Rhombus (or kite? But diagonals given — so use diagonal formula)
Diagonals: d1 = 18 mm, d2 = 6 mm
Area = ½ × d1 × d2 = ½ × 18 × 6 = 9 × 6 =
54 mm²
But wait — we need perimeter too. The rhombus has 4 equal sides. Each side can be found using half-diagonals as legs of a right triangle.
Half of 18 = 9 mm, half of 6 = 3 mm
Side = √(9² + 3²) = √(81 + 9) = √90 ≈ 9.4868 mm
Perimeter = 4 × side ≈ 4 × 9.4868 ≈
37.95 mm (we’ll round to two decimals:
37.95 mm)
*Note: If this is intended to be a kite with unequal adjacent sides, but diagram shows all sides marked equal → rhombus.*
Wait — looking again: the figure has diagonals intersecting at right angles, and all four sides are marked with same tick marks → yes, rhombus. So above is correct.
But let me double-check: sometimes worksheets assume you just add the outer edges if labeled. Here no side lengths are given except via diagonals. So we must calculate side from diagonals.
√(9² + 3²) = √(81+9)=√90=3√10≈9.4868 → times 4 = 37.947 →
37.95 mm
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Problem 6: Trapezoid
Bases: top = 8.7 in, bottom = 12.7 in, height = 4.2 in, left side = 5.8 in, right side = 3.8 in
Area = ½ × (8.7 + 12.7) × 4.2 = ½ × 21.4 × 4.2
First, 21.4 × 4.2:
20 × 4.2 = 84
1.4 × 4.2 = 5.88
Total = 84 + 5.88 = 89.88
Then half: 89.88 ÷ 2 =
44.94 in²
Perimeter = 8.7 + 12.7 + 5.8 + 3.8 = let’s add:
8.7 + 12.7 = 21.4
5.8 + 3.8 = 9.6
Total = 21.4 + 9.6 =
31.0 in
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Problem 7: Rectangle
Length = 9.9 ft, Width = 4.2 ft
Area = 9.9 × 4.2
Breakdown: 10 × 4.2 = 42, minus 0.1 × 4.2 = 0.42 → 42 - 0.42 =
41.58 ft²
Perimeter = 2 × (9.9 + 4.2) = 2 × 14.1 =
28.2 ft
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Problem 8: Parallelogram
Base = 6.8 m, Height = 8.8 m, Side = 9.8 m
Area = base × height = 6.8 × 8.8
Compute: 6 × 8.8 = 52.8, 0.8 × 8.8 = 7.04 → total = 52.8 + 7.04 =
59.84 m²
Perimeter = 2 × (base + side) = 2 × (6.8 + 9.8) = 2 × 16.6 =
33.2 m
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Now let’s compile final answers neatly.
Final Answer:
1. Area = 43.56 yd², Perimeter = 26.4 yd
2. Area = 30.69 in², Perimeter = 25.2 in
3. Area = 146.08 m², Perimeter = 47.0 m
4. Area = 100 cm², Perimeter = 43 cm
5. Area = 54 mm², Perimeter = 37.95 mm
6. Area = 44.94 in², Perimeter = 31.0 in
7. Area = 41.58 ft², Perimeter = 28.2 ft
8. Area = 59.84 m², Perimeter = 33.2 m
Parent Tip: Review the logic above to help your child master the concept of area and perimeter worksheet grade 7.
