Area and Perimeter of Quadrilateral Worksheet - Practice finding area and perimeter for various quadrilaterals.

Let’s solve each problem one by one. We’ll find the area and perimeter for each quadrilateral using the right formulas.

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Problem 1: Square (all sides equal, marked with ticks)

Side = 6.6 yd

- Area of square = side × side = 6.6 × 6.6
→ 6.6 × 6.6 = 43.56 sq yd

- Perimeter = 4 × side = 4 × 6.6 = 26.4 yd

✔ Check: 6.6 + 6.6 + 6.6 + 6.6 = 26.4 ✔️

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Problem 2: Rectangle

Length = 9.3 in, Width = 3.3 in

- Area = length × width = 9.3 × 3.3
→ 9.3 × 3 = 27.9; 9.3 × 0.3 = 2.79 → total = 27.9 + 2.79 = 30.69 sq in

- Perimeter = 2 × (length + width) = 2 × (9.3 + 3.3) = 2 × 12.6 = 25.2 in

✔ Check: 9.3 + 3.3 + 9.3 + 3.3 = 25.2 ✔️

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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 compute:
16.6 × 8 = 132.8
16.6 × 0.8 = 13.28
Total = 132.8 + 13.28 = 146.08 sq m

- Perimeter = 2 × (base + side) = 2 × (16.6 + 6.9) = 2 × 23.5 = 47.0 m

✔ Check: 16.6 + 6.9 + 16.6 + 6.9 = 47.0 ✔️

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Problem 4: Trapezoid

Top base = 7 cm, Bottom base = 18 cm, Height = 8 cm, Legs = 9 cm each

- Area = ½ × (sum of bases) × height = ½ × (7 + 18) × 8 = ½ × 25 × 8 = 12.5 × 8 = 100 sq cm

- Perimeter = sum of all sides = 7 + 18 + 9 + 9 = 43 cm

✔ Check: 7+18=25, 9+9=18, 25+18=43 ✔️

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Problem 5: Rhombus (or kite? but diagonals given)

Diagonals: d1 = 18 mm, d2 = 6 mm
Also, side is labeled 8 mm — let’s use diagonals for area since they’re perpendicular.

Actually, looking at diagram: it's a rhombus with diagonals 18 mm and 6 mm. The 8 mm might be a red herring or mislabel? But wait — if diagonals are 18 and 6, then half-diagonals are 9 and 3. Then side should be √(9² + 3²) = √(81+9)=√90≈9.49 — not 8. So maybe the 8 mm is the side? But then we don’t have height.

Wait — actually, in the diagram, it shows two diagonals intersecting at right angles: one is 18 mm (horizontal), one is 6 mm (vertical). And each side is marked as 8 mm? That doesn’t match mathematically. But perhaps the 8 mm is just labeling the side, and we should use diagonals for area.

Standard formula for rhombus when diagonals known: Area = (d1 × d2)/2

So: (18 × 6)/2 = 108/2 = 54 sq mm

Perimeter: if all sides are 8 mm (as marked with same tick marks), then perimeter = 4 × 8 = 32 mm

Even though geometrically inconsistent, we go by what’s labeled: sides are 8 mm each.

✔ So: Area = 54 sq mm, Perimeter = 32 mm

*(Note: In real geometry, if diagonals are 18 and 6, side can't be 8 — but for worksheet purposes, follow labels.)*

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Problem 6: Trapezoid

Top base = 8.7 in, Bottom base = 12.7 in, Height = 4.2 in, Left leg = 5.8 in, Right leg = 3.8 in

- Area = ½ × (8.7 + 12.7) × 4.2 = ½ × 21.4 × 4.2
First: 21.4 × 4.2
21.4 × 4 = 85.6
21.4 × 0.2 = 4.28
Total = 85.6 + 4.28 = 89.88
Half of that: 89.88 ÷ 2 = 44.94 sq in

- Perimeter = 8.7 + 12.7 + 5.8 + 3.8
Add step by step:
8.7 + 12.7 = 21.4
5.8 + 3.8 = 9.6
Total = 21.4 + 9.6 = 31.0 in

✔ Check: All sides added correctly ✔️

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Problem 7: Rectangle

Width = 4.2 ft, Height = 9.9 ft

- Area = 4.2 × 9.9
Compute: 4.2 × 10 = 42, minus 4.2 × 0.1 = 0.42 → 42 - 0.42 = 41.58 sq ft
Or directly: 4.2 × 9.9 = (4 × 9.9) + (0.2 × 9.9) = 39.6 + 1.98 = 41.58 ✔️

- Perimeter = 2 × (4.2 + 9.9) = 2 × 14.1 = 28.2 ft

✔ Check: 4.2 + 9.9 + 4.2 + 9.9 = 28.2 ✔️

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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 = 54.4
6.8 × 0.8 = 5.44
Total = 54.4 + 5.44 = 59.84 sq m

- Perimeter = 2 × (base + side) = 2 × (6.8 + 9.8) = 2 × 16.6 = 33.2 m

✔ Check: 6.8 + 9.8 + 6.8 + 9.8 = 33.2 ✔️

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## Final Answer:

1. Area = 43.56 sq yd, Perimeter = 26.4 yd
2. Area = 30.69 sq in, Perimeter = 25.2 in
3. Area = 146.08 sq m, Perimeter = 47.0 m
4. Area = 100 sq cm, Perimeter = 43 cm
5. Area = 54 sq mm, Perimeter = 32 mm
6. Area = 44.94 sq in, Perimeter = 31.0 in
7. Area = 41.58 sq ft, Perimeter = 28.2 ft
8. Area = 59.84 sq m, Perimeter = 33.2 m