Scale Drawings Math Example 4

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Example 4

hard
A park is drawn on a map using a scale of 22 cm :300: 300 m. On the map, the park is a rectangle 55 cm by 33 cm. Find the actual area of the park in square meters and in hectares (1 hectare = 10,000 m²).

Solution

  1. 1
    Step 1: Find the scale factor for lengths: 22 cm =300= 300 m, so 11 cm =150= 150 m.
  2. 2
    Step 2: Convert map dimensions to actual: Length =5×150=750= 5 \times 150 = 750 m; Width =3×150=450= 3 \times 150 = 450 m.
  3. 3
    Step 3: Actual area =750×450=337,500= 750 \times 450 = 337{,}500 m².
  4. 4
    Step 4: Convert to hectares: 337,500÷10,000=33.75337{,}500 \div 10{,}000 = 33.75 hectares.

Answer

337,500337{,}500 m² =33.75= 33.75 hectares
The linear scale factor is 150 (each cm represents 150 m). Area scales by the square of the linear factor: the map area of 15 cm² scales to 15 × 150² = 15 × 22,500 = 337,500 m². Converting to hectares gives 33.75 ha.

About Scale Drawings

Creating or interpreting drawings and models where every length is multiplied by the same constant (the scale factor), preserving shape while changing size.

Learn more about Scale Drawings →

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Example 3 easy

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