To find the area of the entire farm on the scale drawing, you can use the formula for the area of a rectangle, which is given by:
\[ \text{Area} = \text{length} \times \text{width} \]
For the farm, the dimensions are:
- Length = 50 cm
- Width = 20 cm
Calculating the area of the entire farm:
\[ \text{Area of the farm} = 50 , \text{cm} \times 20 , \text{cm} = 1000 , \text{square cm} \]
Next, calculate the area of the vegetable garden. The dimensions of the vegetable garden are:
- Length = 10 cm
- Width = 10 cm
Calculating the area of the vegetable garden:
\[ \text{Area of the vegetable garden} = 10 , \text{cm} \times 10 , \text{cm} = 100 , \text{square cm} \]
Now, to find the percentage of the farm that the vegetable garden occupies, you can use the following formula:
\[ \text{Percentage} = \left( \frac{\text{Area of the vegetable garden}}{\text{Area of the entire farm}} \right) \times 100 \]
Substituting the areas we calculated:
\[ \text{Percentage} = \left( \frac{100 , \text{square cm}}{1000 , \text{square cm}} \right) \times 100 = 10% \]
So, the area of the entire farm is 1000 square cm, and the vegetable garden occupies 10% of the farm.