A lake on a map has an area of 6.16 cm2. The scale of the map is 1:50000. What is the actual area of the lake in hectares?

The linear scale is $1:50000$, meaning $1 \text{ cm}$ on the map represents $50000 \text{ cm}$ on the ground.
The area scale factor is the square of the linear scale factor:

$$\text{Area Scale Factor} = (50000)^2 = 2,500,000,000$$

So, $1 \text{ cm}^2$ on the map represents $2,500,000,000 \text{ cm}^2$ on the ground.

$$\text{Actual Area in cm}^2 = \text{Area on map} \times \text{Area Scale Factor}$$ $$\text{Actual Area in cm}^2 = 6.16 \text{ cm}^2 \times 2,500,000,000$$ $$\text{Actual Area in cm}^2 = 15,400,000,000 \text{ cm}^2$$

Since $1 \text{ m} = 100 \text{ cm}$, then $1 \text{ m}^2 = (100 \text{ cm})^2 = 10,000 \text{ cm}^2$.

$$\text{Actual Area in m}^2 = \frac{15,400,000,000 \text{ cm}^2}{10,000 \text{ cm}^2/\text{m}^2}$$ $$\text{Actual Area in m}^2 = 1,540,000 \text{ m}^2$$

Since $1 \text{ hectare} = 10,000 \text{ m}^2$.

$$\text{Actual Area in hectares} = \frac{1,540,000 \text{ m}^2}{10,000 \text{ m}^2/\text{hectare}}$$ $$\text{Actual Area in hectares} = 154 \text{ hectares}$$

The actual area of the lake is $154 \text{ hectares}$.