Let's solve each problem step by step and calculate the
area of each quadrilateral. We’ll use the appropriate formulas for each shape.
---
🔷 Formulas Used:
1.
Square:
$$
\text{Area} = \text{side} \times \text{side}
$$
2.
Rectangle:
$$
\text{Area} = \text{length} \times \text{width}
$$
3.
Parallelogram:
$$
\text{Area} = \text{base} \times \text{height}
$$
4.
Trapezoid:
$$
\text{Area} = \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height}
$$
---
Now, let’s go through each figure:
---
1. Square (4 cm × 4 cm)
$$
\text{Area} = 4 \times 4 = 16\ \text{cm}^2
$$
✔ Answer: 16 cm²
---
2. Square (12 mm × 12 mm)
$$
\text{Area} = 12 \times 12 = 144\ \text{mm}^2
$$
✔ Answer: 144 mm²
---
3. Rectangle (6 cm × 11 cm)
$$
\text{Area} = 6 \times 11 = 66\ \text{cm}^2
$$
✔ Answer: 66 cm²
---
4. Parallelogram (base = 12 m, height = 3 m)
$$
\text{Area} = 12 \times 3 = 36\ \text{m}^2
$$
✔ Answer: 36 m²
---
5. Rectangle (9 ft × 7 ft)
$$
\text{Area} = 9 \times 7 = 63\ \text{ft}^2
$$
✔ Answer: 63 ft²
---
6. Trapezoid (bases = 8 cm and 14 cm, height = 6 cm)
$$
\text{Area} = \frac{1}{2} \times (8 + 14) \times 6 = \frac{1}{2} \times 22 \times 6 = 11 \times 6 = 66\ \text{cm}^2
$$
✔ Answer: 66 cm²
---
7. Rectangle (5 mm × 7 mm)
$$
\text{Area} = 5 \times 7 = 35\ \text{mm}^2
$$
✔ Answer: 35 mm²
---
8. Square (9 m × 9 m)
$$
\text{Area} = 9 \times 9 = 81\ \text{m}^2
$$
✔ Answer: 81 m²
---
9. Parallelogram (base = 18 cm, height = 10 mm)
⚠️
Units differ! Convert 10 mm to cm:
$$
10\ \text{mm} = 1\ \text{cm}
$$
Now:
$$
\text{Area} = 18 \times 1 = 18\ \text{cm}^2
$$
✔ Answer: 18 cm²
---
10. Trapezoid (bases = 27 cm and 15 cm, height = 5 cm)
$$
\text{Area} = \frac{1}{2} \times (27 + 15) \times 5 = \frac{1}{2} \times 42 \times 5 = 21 \times 5 = 105\ \text{cm}^2
$$
✔ Answer: 105 cm²
---
✔ Final Answers:
| Problem | Area |
|--------|------|
| 1 | 16 cm² |
| 2 | 144 mm² |
| 3 | 66 cm² |
| 4 | 36 m² |
| 5 | 63 ft² |
| 6 | 66 cm² |
| 7 | 35 mm² |
| 8 | 81 m² |
| 9 | 18 cm² |
| 10 | 105 cm² |
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Let me know if you'd like this formatted as a printable answer sheet!
Parent Tip: Review the logic above to help your child master the concept of quadrilateral area worksheet.
