A model of a ship is made to a scale of `1:160`. Find:
the area of the deck of the ship, if the area of the deck of its model is `1.2m^(2)`

Answer

To find the area of the deck of the ship based on the model's area and the scale, we can follow these steps:

### Step 1: Understand the scale
The scale given is 1:160, which means that 1 unit of measurement on the model corresponds to 160 units on the actual ship.

### Step 2: Calculate the area scale factor
Since the scale is in terms of length, we need to square the scale factor to find the area scale factor. The area scale factor will be:
\[ \text{Area scale factor} = (160)^2 = 25600 \]

### Step 3: Calculate the area of the actual deck
Given that the area of the deck of the model is \(1.2 \, m^2\), we can find the area of the actual deck by multiplying the area of the model by the area scale factor:
\[ \text{Area of the actual deck} = \text{Area of the model} \times \text{Area scale factor} \]
\[ \text{Area of the actual deck} = 1.2 \, m^2 \times 25600 \]

### Step 4: Perform the calculation
Now, we will calculate the area of the actual deck:
\[ \text{Area of the actual deck} = 1.2 \times 25600 = 30720 \, m^2 \]

### Conclusion
The area of the deck of the ship is \(30720 \, m^2\).

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