A water dam is drawn using a scale of 1 : 2 500. Determine the scale used in drawing the trench is 10 cm by 1 cm, cm long and 8 cm wide, find total area in hectares that is required for the construction of the dam.

The height of the tree on paper is $10 \text{ cm}$.
The scale used is $1:500$. This means $1 \text{ cm}$ on paper represents $500 \text{ cm}$ in actual height.

Actual height = Diagram height $\times$ Scale factor

Since $1 \text{ m} = 100 \text{ cm}$:

The actual height of the tree is $\boxed{\text{50 m}}$.

2.

Actual length = $50 \text{ m}$
Actual depth = $2.5 \text{ m}$
Diagram length = $10 \text{ cm}$
Diagram depth = $0.5 \text{ cm}$

Actual length in cm = $50 \text{ m} \times 100 \text{ cm/m} = 5000 \text{ cm}$
Actual depth in cm = $2.5 \text{ m} \times 100 \text{ cm/m} = 250 \text{ cm}$

Scale = Diagram length : Actual length

To express this in the form $1:N$, divide both sides by 10:

(We can verify this with depth: $0.5 \text{ cm} : 250 \text{ cm}$. Divide both by 0.5: $1 : \frac{250}{0.5} = 1 : 500$).
The scale used is $\boxed{1:500}$.

3.

Diagram length = $10 \text{ cm}$
Diagram width = $8 \text{ cm}$
Scale used = $1:2500$

Actual length = Diagram length $\times$ Scale factor

Actual width = Diagram width $\times$ Scale factor

Actual length in m = $\frac{25000 \text{ cm}}{100 \text{ cm/m}} = 250 \text{ m}$
Actual width in m = $\frac{20000 \text{ cm}}{100 \text{ cm/m}} = 200 \text{ m}$

Area = Actual length $\times$ Actual width

Since $1 \text{ hectare} = 10000 \text{ m}^2$:

The total area required for the construction of the dam is $\boxed{\text{5 hectares}}$.