Question

The rectangle shows the outline of a campsite in a national forest. The dimensions of the rectangle are 3m x 4m. 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?

Answer 1

To determine the area of the scale drawing, we first need to find the scale factor between the original dimensions of the rectangle and the dimensions of the scale drawing.

The original rectangle has dimensions of 3 meters (width) and 4 meters (length). The longer side (4 meters) is scaled down to 1 meter in the drawing.

**Step 1: Calculate the scale factor for the longer side.**
\[
\text{Scale factor} = \frac{\text{Length in scale drawing}}{\text{Original length}} = \frac{1 \text{ m}}{4 \text{ m}} = \frac{1}{4}
\]

**Step 2: Apply this scale factor to the shorter side (3 meters).**
To find the corresponding length of the shorter side in the scale drawing, we multiply the original width by the scale factor:
\[
\text{Width in scale drawing} = \text{Original width} \times \text{Scale factor} = 3 \text{ m} \times \frac{1}{4} = \frac{3}{4} \text{ m}
\]

**Step 3: Calculate the area of the scale drawing.**
The area of a rectangle is given by the formula:
\[
\text{Area} = \text{Length} \times \text{Width}
\]
For the scale drawing:
\[
\text{Area} = 1 \text{ m} \times \frac{3}{4} \text{ m} = \frac{3}{4} \text{ m}^2
\]

Thus, the area of the scale drawing is \(\frac{3}{4}\) square meters.

**Final Answer:**
\(\frac{3}{4} \text{ m}^2\)