The scale of a map is given as 1 : 10000 . On the map, a forest occupies a rectangular region measuring `10 cm xx 100` cm. 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 will 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: Find the Actual Length
The length of the forest on the map is given as 10 cm. To find the actual length, we multiply the length on the map by the scale factor:
\[ \text{Actual Length} = \text{Length on map} \times \text{Scale factor} = 10 \, \text{cm} \times 10,000 = 100,000 \, \text{cm} \]
Now, convert cm to km (since 1 km = 100,000 cm):
\[ \text{Actual Length} = \frac{100,000 \, \text{cm}}{100,000} = 1 \, \text{km} \]

### Step 3: Find the Actual Breadth
The breadth of the forest on the map is given as 100 cm. Similarly, we find the actual breadth:
\[ \text{Actual Breadth} = \text{Breadth on map} \times \text{Scale factor} = 100 \, \text{cm} \times 10,000 = 1,000,000 \, \text{cm} \]
Convert cm to km:
\[ \text{Actual Breadth} = \frac{1,000,000 \, \text{cm}}{100,000} = 10 \, \text{km} \]

### Step 4: Calculate the Actual Area
Now that we have the actual dimensions, we can calculate the area of the forest:
\[ \text{Area} = \text{Actual Length} \times \text{Actual Breadth} = 1 \, \text{km} \times 10 \, \text{km} = 10 \, \text{km}^2 \]

### Final Answer
The actual area of the forest is \(10 \, \text{km}^2\).

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