Estimating the area of irregular shapes using a grid method.

To solve the problem of estimating the area of irregular shapes using the grid method, we need to count the whole squares and part squares that are covered by each shape. Here's a step-by-step explanation for each shape:

Shape 1 (Light Blue)

- Whole squares: Count the fully shaded squares.
- Part squares: Count the partially shaded squares. Typically, if a square is more than half shaded, it can be counted as a whole square; otherwise, it can be approximated as half.

#### Estimation:
- Whole squares: 12
- Part squares: 8 (each part square is approximately half, so 8 parts = 4 whole squares)
- Approximate area: \( 12 + 4 = 16 \, \text{cm}^2 \)

Shape 2 (Purple)

- Whole squares: Count the fully shaded squares.
- Part squares: Count the partially shaded squares.

#### Estimation:
- Whole squares: 5
- Part squares: 6 (each part square is approximately half, so 6 parts = 3 whole squares)
- Approximate area: \( 5 + 3 = 8 \, \text{cm}^2 \)

Shape 3 (Pink)

- Whole squares: Count the fully shaded squares.
- Part squares: Count the partially shaded squares.

#### Estimation:
- Whole squares: 10
- Part squares: 10 (each part square is approximately half, so 10 parts = 5 whole squares)
- Approximate area: \( 10 + 5 = 15 \, \text{cm}^2 \)

Shape 4 (Yellow)

- Whole squares: Count the fully shaded squares.
- Part squares: Count the partially shaded squares.

#### Estimation:
- Whole squares: 6
- Part squares: 4 (each part square is approximately half, so 4 parts = 2 whole squares)
- Approximate area: \( 6 + 2 = 8 \, \text{cm}^2 \)

Shape 5 (Dark Purple)

- Whole squares: Count the fully shaded squares.
- Part squares: Count the partially shaded squares.

#### Estimation:
- Whole squares: 10
- Part squares: 8 (each part square is approximately half, so 8 parts = 4 whole squares)
- Approximate area: \( 10 + 4 = 14 \, \text{cm}^2 \)

Shape 6 (Blue)

- Whole squares: Count the fully shaded squares.
- Part squares: Count the partially shaded squares.

#### Estimation:
- Whole squares: 6
- Part squares: 6 (each part square is approximately half, so 6 parts = 3 whole squares)
- Approximate area: \( 6 + 3 = 9 \, \text{cm}^2 \)

Final Answers

1. Light Blue: \( 16 \, \text{cm}^2 \)
2. Purple: \( 8 \, \text{cm}^2 \)
3. Pink: \( 15 \, \text{cm}^2 \)
4. Yellow: \( 8 \, \text{cm}^2 \)
5. Dark Purple: \( 14 \, \text{cm}^2 \)
6. Blue: \( 9 \, \text{cm}^2 \)

Boxed Final Answer

\[
\boxed{
\begin{array}{ccc}
\text{Shape 1} & \text{Shape 2} & \text{Shape 3} \\
16 \, \text{cm}^2 & 8 \, \text{cm}^2 & 15 \, \text{cm}^2 \\
\text{Shape 4} & \text{Shape 5} & \text{Shape 6} \\
8 \, \text{cm}^2 & 14 \, \text{cm}^2 & 9 \, \text{cm}^2 \\
\end{array}
}
\]