On a map drawn to a scale of `1:50,000`, a rectangular plot of alnd ABCD has the following dimensions. AB = 6 cm, BCv = 8 cm and all angles are right angles. Find :
(ii) the actual area of the plot in sq. km.

Answer

To find the actual area of the rectangular plot of land ABCD based on the given dimensions on a map with a scale of 1:50,000, we can follow these steps:

### Step 1: Understand the scale
The scale of 1:50,000 means that 1 cm on the map represents 50,000 cm in reality.

### Step 2: Convert the dimensions from cm to km
- The length AB is given as 6 cm. To find the actual length, we multiply by the scale factor:
\[ \text{Actual length of AB} = 6 \, \text{cm} \times 50,000 \, \text{cm/cm} = 300,000 \, \text{cm} \]
- Convert centimeters to kilometers:
\[ 300,000 \, \text{cm} = \frac{300,000}{100,000} \, \text{km} = 3 \, \text{km} \]

- The width BC is given as 8 cm. Similarly, we calculate the actual width:
\[ \text{Actual width of BC} = 8 \, \text{cm} \times 50,000 \, \text{cm/cm} = 400,000 \, \text{cm} \]
- Convert centimeters to kilometers:
\[ 400,000 \, \text{cm} = \frac{400,000}{100,000} \, \text{km} = 4 \, \text{km} \]

### Step 3: Calculate the area of the rectangular plot
The area \( A \) of a rectangle is given by the formula:
\[ A = \text{length} \times \text{width} \]
Substituting the actual dimensions:
\[ A = 3 \, \text{km} \times 4 \, \text{km} = 12 \, \text{km}^2 \]

### Final Answer
The actual area of the plot is \( 12 \, \text{km}^2 \).

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