Scale Drawing - SpecialEdSimplified - Free Printable

Let's solve both problems step by step using scale drawings and the concept of area scaling.

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🔷 Problem 5: Area of a Piece of Land

#### Given:
- Scale drawing dimensions: 4 cm × 7 cm
- Scale: 1 cm : 10 m
- We are to find the actual area of the land.

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#### Step 1: Convert scale drawing dimensions to actual dimensions

Since 1 cm on the drawing = 10 m in real life, we multiply each dimension:

- Length:
$ 4 \text{ cm} \times 10 \text{ m/cm} = 40 \text{ m} $

- Width:
$ 7 \text{ cm} \times 10 \text{ m/cm} = 70 \text{ m} $

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#### Step 2: Calculate actual area

$$
\text{Actual Area} = 40 \text{ m} \times 70 \text{ m} = 2800 \text{ m}^2
$$

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#### Fill in the table:

| Plan | × | Scale | × | Actual |
|------|---|--------|---|--------|
| 4 | × | 7 | × | 100 | = | 2800 |

> ✔ Why 100? Because when converting area, we must square the scale factor.
> The scale is 1 cm : 10 m, so area scale is:
> $$
> (10)^2 = 100
> $$
> So, the area is scaled by 100 times.

Alternatively:
- Plan area: $ 4 \times 7 = 28 \text{ cm}^2 $
- Multiply by scale factor squared: $ 28 \times 100 = 2800 \text{ m}^2 $

✔ Final Answer: 2800 m²

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🔷 Problem 6: Area of the Real Train’s Side Wall

#### Given:
- Model wall dimensions: 2 cm × 3 cm
- Scale: 1 cm : 3 m
- Find actual area of the train’s side wall.

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#### Step 1: Convert dimensions to actual size

- Length:
$ 2 \text{ cm} \times 3 \text{ m/cm} = 6 \text{ m} $

- Width:
$ 3 \text{ cm} \times 3 \text{ m/cm} = 9 \text{ m} $

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#### Step 2: Calculate actual area

$$
\text{Actual Area} = 6 \text{ m} \times 9 \text{ m} = 54 \text{ m}^2
$$

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#### Fill in the table:

| Plan | × | Scale | × | Actual |
|------|---|--------|---|--------|
| 2 | × | 3 | × | 9 | = | 54 |

> ✔ Why 9? Because the scale factor for area is $ (3)^2 = 9 $.
> So, area scales by 9 times.

Alternatively:
- Plan area: $ 2 \times 3 = 6 \text{ cm}^2 $
- Multiply by scale factor squared: $ 6 \times 9 = 54 \text{ m}^2 $

✔ Final Answer: 54 m²

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✔ Summary of Answers:

#### Problem 5:
- Plan: 4 × 7 = 28 cm²
- Scale factor (area): $ (10)^2 = 100 $
- Actual area: $ 28 \times 100 = 2800 \text{ m}^2 $

➡️ Table:
4 × 7 × 100 = 2800

#### Problem 6:
- Plan: 2 × 3 = 6 cm²
- Scale factor (area): $ (3)^2 = 9 $
- Actual area: $ 6 \times 9 = 54 \text{ m}^2 $

➡️ Table:
2 × 3 × 9 = 54

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📌 Key Concept:

When working with area and scale drawings, remember:
> Area scale factor = (linear scale factor)²

So if 1 cm → 10 m, then 1 cm² → 100 m².

This is why we multiply by 100 or 9, not just 10 or 3.

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✔ Final Answers:
- Problem 5: 2800 m²
- Problem 6: 54 m²