Worksheet for converting metric units of area, including diagrams and practice exercises.

Let's solve each of the conversion problems step by step using the metric unit conversion rules for area provided in the image.

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🔁 Key Conversion Rules (Area):

- $ 1 \text{ cm}^2 = 100 \text{ mm}^2 $
- $ 1 \text{ m}^2 = 100 \text{ cm}^2 $
- $ 1 \text{ m}^2 = 10000 \text{ mm}^2 $
- $ 1 \text{ dm}^2 = 100 \text{ cm}^2 $
- $ 1 \text{ m}^2 = 100 \text{ dm}^2 $
- $ 1 \text{ km}^2 = 1,000,000 \text{ m}^2 $
- $ 1 \text{ ha} = 10,000 \text{ m}^2 $

We will use these to convert between units.

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✔ Solutions:

#### a. $ 7 \text{ cm}^2 = ? \text{ mm}^2 $
$$
7 \times 100 = 700 \text{ mm}^2
$$

> ✔ Answer: $ 700 \text{ mm}^2 $

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#### b. $ 2.5 \text{ m}^2 = ? \text{ cm}^2 $
$$
2.5 \times 10000 = 25,000 \text{ cm}^2
$$

> ✔ Answer: $ 25,000 \text{ cm}^2 $

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#### c. $ 2.4 \text{ m}^2 = ? \text{ mm}^2 $
$$
2.4 \times 1,000,000 = 2,400,000 \text{ mm}^2
$$

> ✔ Answer: $ 2,400,000 \text{ mm}^2 $

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#### d. $ 1.8 \text{ dm}^2 = ? \text{ mm}^2 $
First, $ 1 \text{ dm}^2 = 100 \text{ cm}^2 = 10,000 \text{ mm}^2 $
$$
1.8 \times 10,000 = 18,000 \text{ mm}^2
$$

> ✔ Answer: $ 18,000 \text{ mm}^2 $

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#### e. $ 9000 \text{ mm}^2 = ? \text{ cm}^2 $
$$
9000 \div 100 = 90 \text{ cm}^2
$$

> ✔ Answer: $ 90 \text{ cm}^2 $

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#### f. $ 90 \text{ cm}^2 = ? \text{ m}^2 $
$$
90 \div 10,000 = 0.009 \text{ m}^2
$$

> ✔ Answer: $ 0.009 \text{ m}^2 $

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#### g. $ 17,000 \text{ cm}^2 = ? \text{ dm}^2 $
$$
17,000 \div 100 = 170 \text{ dm}^2
$$

> ✔ Answer: $ 170 \text{ dm}^2 $

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#### h. $ 4000 \text{ dm}^2 = ? \text{ m}^2 $
$$
4000 \div 100 = 40 \text{ m}^2
$$

> ✔ Answer: $ 40 \text{ m}^2 $

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#### i. $ 26 \text{ cm}^2 = ? \text{ m}^2 $
$$
26 \div 10,000 = 0.0026 \text{ m}^2
$$

> ✔ Answer: $ 0.0026 \text{ m}^2 $

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#### j. $ 0.003 \text{ m}^2 = ? \text{ cm}^2 $
$$
0.003 \times 10,000 = 30 \text{ cm}^2
$$

> ✔ Answer: $ 30 \text{ cm}^2 $

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#### k. $ 5 \text{ km}^2 = ? \text{ m}^2 $
$$
5 \times 1,000,000 = 5,000,000 \text{ m}^2
$$

> ✔ Answer: $ 5,000,000 \text{ m}^2 $

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#### l. $ 800 \text{ mm}^2 = ? \text{ dm}^2 $
Convert step-by-step:
- $ 800 \text{ mm}^2 \to \text{cm}^2 $: $ 800 \div 100 = 8 \text{ cm}^2 $
- $ 8 \text{ cm}^2 \to \text{dm}^2 $: $ 8 \div 100 = 0.08 \text{ dm}^2 $

> ✔ Answer: $ 0.08 \text{ dm}^2 $

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#### m. $ 0.09 \text{ m}^2 = ? \text{ mm}^2 $
$$
0.09 \times 1,000,000 = 90,000 \text{ mm}^2
$$

> ✔ Answer: $ 90,000 \text{ mm}^2 $

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#### n. $ 800,000 \text{ m}^2 = ? \text{ hm}^2 $
Note: $ 1 \text{ hm}^2 = 10,000 \text{ m}^2 $
$$
800,000 \div 10,000 = 80 \text{ hm}^2
$$

> ✔ Answer: $ 80 \text{ hm}^2 $

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#### o. $ 400,000 \text{ m}^2 = ? \text{ km}^2 $
$$
400,000 \div 1,000,000 = 0.4 \text{ km}^2
$$

> ✔ Answer: $ 0.4 \text{ km}^2 $

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#### p. $ 40 \text{ hm}^2 = ? \text{ m}^2 $
$$
40 \times 10,000 = 400,000 \text{ m}^2
$$

> ✔ Answer: $ 400,000 \text{ m}^2 $

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#### q. $ 0.7 \text{ km}^2 = ? \text{ m}^2 $
$$
0.7 \times 1,000,000 = 700,000 \text{ m}^2
$$

> ✔ Answer: $ 700,000 \text{ m}^2 $

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#### r. $ 8 \text{ ha} = ? \text{ km}^2 $
Note: $ 1 \text{ ha} = 10,000 \text{ m}^2 $, and $ 1 \text{ km}^2 = 1,000,000 \text{ m}^2 $
So:
$$
8 \times 10,000 = 80,000 \text{ m}^2 \\
80,000 \div 1,000,000 = 0.08 \text{ km}^2
$$

> ✔ Answer: $ 0.08 \text{ km}^2 $

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📌 Final Answers Summary:

| Item | Answer |
|------|--------|
| a | 700 mm² |
| b | 25,000 cm² |
| c | 2,400,000 mm² |
| d | 18,000 mm² |
| e | 90 cm² |
| f | 0.009 m² |
| g | 170 dm² |
| h | 40 m² |
| i | 0.0026 m² |
| j | 30 cm² |
| k | 5,000,000 m² |
| l | 0.08 dm² |
| m | 90,000 mm² |
| n | 80 hm² |
| o | 0.4 km² |
| p | 400,000 m² |
| q | 700,000 m² |
| r | 0.08 km² |

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✔ All conversions are based on the metric system relationships and consistent with the diagram provided.

Let me know if you'd like this as a printable worksheet or with explanations in a different format!