Question

Sports A soccer field is 91 meters by 46 meters. Make a scale drawing of the field if 1 millimeter represents 1 meter.

Short answer

The scale drawing of the soccer field should measure 91 mm by 46 mm.

Step-by-step solution

Understanding the Scale

The problem states that 1 millimeter on the drawing represents 1 meter in real life. This means that whatever the real dimensions of the soccer field are in meters, those dimensions should be directly converted into millimeters for the drawing.

Converting the Dimensions

The real-life dimensions of the soccer field are 91 meters by 46 meters. According to the scale (1 mm = 1 m), this directly converts to 91 millimeters by 46 millimeters for the scale drawing.

Creating the Scale Drawing

To create the scale drawing, you will need to draw a rectangle that measures 91 mm by 46 mm on paper, using a ruler or appropriate drawing tool. Ensure each side is accurately measured to reflect the proper scale.

Key concepts

Scale Conversion

Scale conversion is a fundamental concept in creating scale drawings. It involves translating real-world measurements into a scaled-down or scaled-up version using a specific ratio. In the exercise, the scale given is "1 millimeter represents 1 meter," which sets the ratio for conversion. This means that for every meter in reality, the drawing should represent it as only 1 millimeter.

To perform a scale conversion, you should:

• Identify the scale factor, which in this case is "1:1000" (since 1 meter = 1000 millimeters).
• Multiply or divide the real-world measurements by the scale factor to convert them appropriately. This exercise converted 91 meters into 91 millimeters and 46 meters into 46 millimeters.

Understanding how to scale down from life-size to a manageable drawing size helps accurately depict large objects on paper, making them easier to analyze and understand.

Measurement

Measurement is integral when working with scale drawings, as it ensures accuracy and precision. In geometry and design, dimensions must be carefully measured to adhere to scale. Here are some points to consider:

• Use appropriate tools, such as a ruler or a grid paper, to measure distances for your drawing.
• Be consistent with the units used. Always verify if dimensions need converting before starting your drawing.
• Recheck your measurements to prevent errors, as even slight inaccuracies can lead to significant deviations in larger projects.

In the exercise, the soccer field's dimensions were given in meters, and they were converted to millimeters to match the scale of the drawing. Precision in measurement ensures the scale drawing remains proportional to its real-world counterpart.

Geometry

Geometry is the study of shapes, sizes, and the properties of space. In scale drawings, understanding geometric principles allows for the accurate depiction of objects and spaces.
Drawing a scale diagram involves creating geometric shapes like rectangles, which represent real-life objects. In this exercise, the soccer field takes the form of a rectangle with specific dimensions.

• Recognize shapes: Geometry helps in identifying and drawing shapes accurately. For the rectangle, the properties include equal opposite sides and right angles.
• Apply geometric concepts to maintain proportionalities in the drawing, ensuring the integrity of the shape and scale.

By using geometry, you accurately construct scale drawings that truthfully represent the original designs, making it a crucial skill in fields such as architecture and engineering.