Calculate and estimate the area of irregular shapes - Master The ... - Free Printable

To estimate the area of irregular shapes on a grid where each square is 1 cm × 1 cm (so each square has an area of 1 cm²), we use the following method:

Method:

- Count the number of whole squares completely inside the shape.
- Count the number of part squares (partial squares) that are partially covered by the shape.
- Estimate the total area using:
> Approximate Area = Whole squares + (Part squares ÷ 2)
*(We divide part squares by 2 because two half-squares make one full square.)*

Let’s go through each shape one by one.

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Shape 1 (Top Left – Light Blue)

- Whole squares: Count all fully enclosed squares.
- Let's count carefully: There are 14 whole squares.
- Part squares: Count partial squares along the edges.
- Approximately 10 part squares.
- Approximate area:
$$
14 + \frac{10}{2} = 14 + 5 = 19\ \text{cm}^2
$$

✔ Answer:
- Whole squares: 14
- Part squares: 10
- Approximate area: 19 cm²

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Shape 2 (Top Right – Purple)

- Whole squares:
- About 8 whole squares.
- Part squares:
- Around 12 part squares.
- Approximate area:
$$
8 + \frac{12}{2} = 8 + 6 = 14\ \text{cm}^2
$$

✔ Answer:
- Whole squares: 8
- Part squares: 12
- Approximate area: 14 cm²

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Shape 3 (Middle Left – Pink)

- Whole squares:
- About 10 whole squares.
- Part squares:
- Around 14 part squares.
- Approximate area:
$$
10 + \frac{14}{2} = 10 + 7 = 17\ \text{cm}^2
$$

✔ Answer:
- Whole squares: 10
- Part squares: 14
- Approximate area: 17 cm²

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Shape 4 (Middle Right – Yellow)

- Whole squares:
- About 6 whole squares.
- Part squares:
- Around 8 part squares.
- Approximate area:
$$
6 + \frac{8}{2} = 6 + 4 = 10\ \text{cm}^2
$$

✔ Answer:
- Whole squares: 6
- Part squares: 8
- Approximate area: 10 cm²

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Shape 5 (Bottom Left – Purple)

- Whole squares:
- About 9 whole squares.
- Part squares:
- Around 10 part squares.
- Approximate area:
$$
9 + \frac{10}{2} = 9 + 5 = 14\ \text{cm}^2
$$

✔ Answer:
- Whole squares: 9
- Part squares: 10
- Approximate area: 14 cm²

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Shape 6 (Bottom Right – Blue)

- Whole squares:
- About 10 whole squares.
- Part squares:
- Around 10 part squares.
- Approximate area:
$$
10 + \frac{10}{2} = 10 + 5 = 15\ \text{cm}^2
$$

✔ Answer:
- Whole squares: 10
- Part squares: 10
- Approximate area: 15 cm²

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✔ Final Answers Summary:

| Shape | Whole Squares | Part Squares | Approximate Area (cm²) |
|-------|----------------|---------------|--------------------------|
| 1 | 14 | 10 | 19 |
| 2 | 8 | 12 | 14 |
| 3 | 10 | 14 | 17 |
| 4 | 6 | 8 | 10 |
| 5 | 9 | 10 | 14 |
| 6 | 10 | 10 | 15 |

> 📌 Note: These are approximations based on visual estimation. Slight variations may occur depending on how you interpret the partial squares, but these values are reasonable estimates.

Let me know if you'd like a diagram-based breakdown!