To draw a scale drawing of a square with sides of 300 meters, using a scale where 1 centimeter represents 50 meters, you need to follow these steps:
1. Understand the Scale Factor:
- The given scale is 1 cm = 50 meters.
2. Determine the Side Length in the Scale Drawing:
- You need to convert the real side length of the square (300 meters) into the scale drawing length (centimeters).
- To do this, divide the actual side length by the scale factor.
- So, [tex]\( 300 \, \text{meters} \div 50 \, \text{meters per centimeter} = 6 \, \text{centimeters} \)[/tex].
3. Calculate the Area in Both Real and Scale Measurements for Reference:
- Area in Real Measurements:
- The area of the square in real measurements is given by the formula for the area of a square, [tex]\( \text{side}^2 \)[/tex].
- In this case, the side of the square is 300 meters.
- Therefore, the area is [tex]\( 300 \, \text{meters} \times 300 \, \text{meters} = 90,000 \, \text{square meters} \)[/tex].
- Area in the Scale Drawing:
- The side length in the scale drawing is 6 centimeters.
- Using the same formula for the area of a square, the area of the scaled-down square is [tex]\( 6 \, \text{centimeters} \times 6 \, \text{centimeters} = 36 \, \text{square centimeters} \)[/tex].
4. Draw the Square:
- Use a ruler to draw a square where each side is 6 centimeters long on your paper. This represents the scaled-down version of the square whose real sides are 300 meters.
By following these steps, you can create an accurate scale drawing of a square with sides of 300 meters using the scale of 1 cm = 50 m. The side length in the scale drawing will be 6 centimeters, the real area of the square is 90,000 square meters, and the area of the scaled drawing is 36 square centimeters.
