The rectangle shows the outline of a campsite in a national forest. Anna makes a scale drawing of the campsite in which the longer side measures 1 meter. What is the area of the scale drawing in square meters?
(1 point)
• 1.33 square meters
• 12 square meters
• 0.75 square meters
• 3.5 square centimeters
To find the area of the scale drawing in square meters, we need to determine both the length and width of the rectangle in the scale drawing.
Since the scale is 1 meter for the longer side, the length of the rectangle in the scale drawing is 1 meter.
Let's assume the actual longer side of the campsite is L meters and the actual shorter side is W meters.
By using these variables, we can create a proportion to determine the length of the shorter side in the scale drawing.
So, \( \dfrac{1}{L} = \dfrac{1}{W} \).
Since we know that the scale is 1 meter for the longer side in the scale drawing, the scale length of the shorter side is \( \dfrac{W}{L} \).
Given that the actual longer side is larger than the actual shorter side, we know that \( L > W \), which implies that \( \dfrac{W}{L} < 1 \).
Now that we know the length and width of the rectangle in the scale drawing, we can calculate the area of the scale drawing by multiplying the length and width:
\[
\text{Area} = 1 \times \dfrac{W}{L} \: \text{square meters}
\]
Since \( \dfrac{W}{L} < 1 \), the area of the scale drawing in square meters is less than 1.
Therefore, the correct answer is:
• 0.75 square meters