The scale of a map is given as 1:10000. On the map, a forest occupies a rectangular region measuring `10cmxx100cm`. The actual area of the forest (in `km^(2)` is)

Options

A. 10
B. 1
C. 1000
D. 100

Answer

To find the actual area of the forest represented on the map, we can follow these steps:

### Step 1: Understand the Scale
The scale of the map is given as 1:10,000. This means that 1 cm on the map represents 10,000 cm in reality.

### Step 2: Convert Map Measurements to Actual Measurements
The forest occupies a rectangular area on the map measuring 10 cm by 100 cm. To find the actual dimensions, we will convert these measurements using the scale.

- **Actual Length**:
\[ \text{Actual Length} = \text{Length on map} \times \text{Scale factor} = 100 \text{ cm} \times 10,000 = 1,000,000 \text{ cm} \]

- **Actual Width**:
\[ \text{Actual Width} = \text{Width on map} \times \text{Scale factor} = 10 \text{ cm} \times 10,000 = 100,000 \text{ cm} \]

### Step 3: Calculate the Actual Area
Now, we can calculate the actual area of the forest using the actual length and width.

\[ \text{Actual Area} = \text{Actual Length} \times \text{Actual Width} = 1,000,000 \text{ cm} \times 100,000 \text{ cm} \]

### Step 4: Convert Area to Square Kilometers
Since the area is currently in square centimeters, we need to convert it to square kilometers.

1 square kilometer = \(10^5 \text{ cm} \times 10^5 \text{ cm} = 10^{10} \text{ cm}^2\).

Thus, we convert the area:
\[ \text{Actual Area in km}^2 = \frac{1,000,000 \text{ cm} \times 100,000 \text{ cm}}{10^{10}} = \frac{100,000,000,000 \text{ cm}^2}{10^{10}} = 10 \text{ km}^2 \]

### Final Answer
The actual area of the forest is **10 km²**.

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