To find the area of the scale drawing, we first need to determine the area of the original rectangle (campsite) based on its dimensions.
The original dimensions of the rectangle are:
- Length = 4 meters (longer side)
- Width = 3 meters (shorter side)
The area \(A\) of the rectangle can be calculated using the formula: \[ A = \text{Length} \times \text{Width} = 4 , \text{m} \times 3 , \text{m} = 12 , \text{m}^2 \]
Now, Anna makes a scale drawing such that the longer side (4 m) is represented as 1 meter in the drawing. To find the scale factor, we divide the length of the drawing by the original length: \[ \text{Scale Factor} = \frac{1 , \text{m}}{4 , \text{m}} = \frac{1}{4} \]
The shorter side (3 m) in the drawing can be calculated using the scale factor. Let's find the length of the shorter side in the scale drawing: \[ \text{Shorter Side Length in Drawing} = 3 , \text{m} \times \frac{1}{4} = 0.75 , \text{m} \]
Now we can calculate the area of the scale drawing using its dimensions: \[ \text{Area of Scale Drawing} = \text{Length} \times \text{Width} = 1 , \text{m} \times 0.75 , \text{m} = 0.75 , \text{m}^2 \]
Thus, the area of the scale drawing is \(0.75\) square meters.
The correct response is: 0.75 square meters