Let's solve each problem step by step, using the appropriate formulas for the area of triangles and quadrilaterals.
---
1) Rectangle
- Dimensions: 6 m × 5.1 m
- Area of rectangle = length × width
$$
\text{Area} = 6 \times 5.1 = 30.6 \text{ m}^2
$$
✔ Answer: 30.6 m²
---
2) Triangle
- Base = 8 yd, Height = 6.4 yd
- Area of triangle = $ \frac{1}{2} \times \text{base} \times \text{height} $
$$
\text{Area} = \frac{1}{2} \times 8 \times 6.4 = 4 \times 6.4 = 25.6 \text{ yd}^2
$$
✔ Answer: 25.6 yd²
---
3) Parallelogram
- Base = 8 m, Height = 3.7 m
- Area of parallelogram = base × height
$$
\text{Area} = 8 \times 3.7 = 29.6 \text{ m}^2
$$
✔ Answer: 29.6 m²
---
4) Rectangle
- Dimensions: 2 yd × 3.1 yd
- Area = length × width
$$
\text{Area} = 2 \times 3.1 = 6.2 \text{ yd}^2
$$
✔ Answer: 6.2 yd²
---
5) Trapezoid
- Bases: 6 mi and 3 mi, Height = 5 mi
- Area of trapezoid = $ \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height} $
$$
\text{Area} = \frac{1}{2} \times (6 + 3) \times 5 = \frac{1}{2} \times 9 \times 5 = 22.5 \text{ mi}^2
$$
✔ Answer: 22.5 mi²
---
6) Triangle
- Base = 6.6 mm, Height = 9 mm
- Area = $ \frac{1}{2} \times 6.6 \times 9 $
$$
= 3.3 \times 9 = 29.7 \text{ mm}^2
$$
✔ Answer: 29.7 mm²
---
7) Square
- Side = 7 mi
- Area = side²
$$
\text{Area} = 7 \times 7 = 49 \text{ mi}^2
$$
✔ Answer: 49 mi²
---
8) Triangle
- Base = 2 km, Height = 3.8 km
- Area = $ \frac{1}{2} \times 2 \times 3.8 = 1 \times 3.8 = 3.8 \text{ km}^2 $
✔ Answer: 3.8 km²
---
9) Parallelogram
- Base = 2 yd, Height = 1 yd
- Area = base × height
$$
\text{Area} = 2 \times 1 = 2 \text{ yd}^2
$$
✔ Answer: 2 yd²
---
10) Trapezoid
- Bases: 4.8 yd and 29.4 ft →
Wait! Units differ!
We need to convert to same unit.
Convert 29.4 ft to yards:
Since 1 yard = 3 feet,
$$
29.4 \div 3 = 9.8 \text{ yd}
$$
Now:
- Base₁ = 4.8 yd
- Base₂ = 9.8 yd
- Height = 8 yd
Area = $ \frac{1}{2} \times (4.8 + 9.8) \times 8 $
$$
= \frac{1}{2} \times 14.6 \times 8 = 7.3 \times 8 = 58.4 \text{ yd}^2
$$
✔ Answer: 58.4 yd²
---
✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 1) | 30.6 m² |
| 2) | 25.6 yd² |
| 3) | 29.6 m² |
| 4) | 6.2 yd² |
| 5) | 22.5 mi² |
| 6) | 29.7 mm² |
| 7) | 49 mi² |
| 8) | 3.8 km² |
| 9) | 2 yd² |
| 10) | 58.4 yd² |
> 🔍
Note: In problem 10, we converted feet to yards before calculating. Always ensure consistent units!
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 triangles and quadrilaterals worksheet.
