On a map, drawn to a scale of 1 : 20000, a rectangular plot of land ABCD has `AB = 24 cm and BC = 32 cm`. Calculate :
the area of the plot in sq. km. 

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the scale of the map
The scale given is 1:20000. This means that 1 cm on the map represents 20000 cm in reality.

### Step 2: Convert the scale to kilometers
To convert the scale from centimeters to kilometers:
1 cm = 20000 cm
Since 1 km = 100000 cm, we can convert 20000 cm to kilometers:
\[ \text{Distance in km} = \frac{20000 \text{ cm}}{100000 \text{ cm/km}} = 0.2 \text{ km} \]
Thus, 1 cm on the map represents 0.2 km in reality.

### Step 3: Calculate the area of the plot on the map
The dimensions of the rectangular plot ABCD are given as:
- AB = 24 cm
- BC = 32 cm

The area \( A \) of a rectangle is calculated using the formula:
\[ A = \text{length} \times \text{width} \]
In this case:
\[ A = AB \times BC = 24 \text{ cm} \times 32 \text{ cm} \]
Calculating this gives:
\[ A = 768 \text{ cm}^2 \]

### Step 4: Convert the area from cm² to km²
Since we know that 1 cm on the map represents 0.2 km in reality, we need to convert the area from cm² to km².
1 cm² on the map represents:
\[ (0.2 \text{ km}) \times (0.2 \text{ km}) = 0.04 \text{ km}^2 \]
Thus, to find the actual area of the plot in km², we multiply the area in cm² by the area conversion factor:
\[ \text{Actual Area} = 768 \text{ cm}^2 \times 0.04 \text{ km}^2/\text{cm}^2 \]
Calculating this gives:
\[ \text{Actual Area} = 30.72 \text{ km}^2 \]

### Final Answer
The area of the plot of land ABCD is **30.72 km²**.

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