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?
A. 1.33 square meters
B. 3.5 square meters
C. 0.75 square meters
D. 12 square meters
To find the area of the scale drawing, we need to calculate the area of the rectangle in the scale drawing using the scale factor.
Since the longer side of the rectangle in the scale drawing measures 1 meter, and the scale factor is unknown, we cannot directly use the length of the actual longer side of the campsite (let's call it L). However, we know that the scale factor is the ratio of the length in the scale drawing to the actual length, which means that:
1 (length in scale drawing) / L (actual length) = scale factor.
This scale factor can vary depending on the ratio of the length in the scale drawing to the actual length, but for simplicity we can say that the scale factor is L. This means that the length of the actual longer side of the campsite is 1/L meters.
Similarly, the width of the actual campsite (W) must be 1/L meters in order to maintain the proportions of the rectangle.
The area of the rectangle is given by:
Area = Length * Width
Area = 1/L * 1/L = 1/L^2
Therefore, the area of the scale drawing in square meters is 1/L^2. This is not an exact value, however, as we do not know the actual length and scale factor. The correct answer depends on the values of L and the scale factor.
Thus, without knowing the actual length of the campsite (L) or the scale factor, we cannot determine the exact area of the scale drawing. The correct answer is not provided in the options (A, B, C, D) given.
choose one of the questions above
If we assume that the scale factor is 1, which would mean that the longer side of the rectangle in the scale drawing represents the same length as the actual longer side of the campsite (1 meter), then the area of the scale drawing would be:
Area = Length * Width
Area = 1 meter * 1 meter
Area = 1 square meter
Therefore, based on the assumption that the scale factor is 1, the area of the scale drawing in square meters would be:
A. 1.33 square meters
So, the closest option provided that matches this scenario is A. 1.33 square meters.