Math Problem Statement

A map of a rectangular park has a length of 4 inches and a width of 6 inches. It uses a scale of 1 inch for every 20 miles. What is the actual area of the park?

Solution

To find the actual area of the park based on the information given, we’ll go through the following steps:

  1. Identify the dimensions on the map:

    • Length: 4 inches
    • Width: 6 inches
  2. Determine the scale:

    • The scale is 1 inch = 20 miles, which means each inch on the map represents 20 miles in real life.
  3. Calculate the actual dimensions of the park:

    • Actual length = 4 inches×20 miles per inch=80 miles4 \text{ inches} \times 20 \text{ miles per inch} = 80 \text{ miles}
    • Actual width = 6 inches×20 miles per inch=120 miles6 \text{ inches} \times 20 \text{ miles per inch} = 120 \text{ miles}
  4. Calculate the actual area:

    • Area = Length × Width
    • Area = 80 miles×120 miles=9600 square miles80 \text{ miles} \times 120 \text{ miles} = 9600 \text{ square miles}

So, the actual area of the park is 9600 square miles.

Would you like more details or have any questions about this solution?

Here are some related questions to explore further:

  1. How would the area change if the scale was 1 inch = 10 miles?
  2. If the map dimensions doubled, what would be the new actual area?
  3. How would you calculate the area if only the map area and scale were given without specific dimensions?
  4. What is the importance of understanding scale in map reading and real-life applications?
  5. Can this method be applied to irregular shapes, and if so, how?

Tip: Always verify the scale when interpreting maps to ensure accuracy in real-world measurements.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area Calculation
Map Scale Conversion

Formulas

Area = Length × Width
Scale Conversion: Actual Dimension = Map Dimension × Scale Factor

Theorems

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Suitable Grade Level

Grades 6-8