Find the area of unshaded region

General
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find the area of unshaded region

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Find the area of the unshaded region

Answer: To find the area of the unshaded region, we need more specific information about the shapes involved, such as the dimensions and the shapes of both the shaded and unshaded regions. However, I can provide a general approach to solving such problems, which typically involves the following steps:

  1. Identify the Total Area of the Shape:

    • Determine the overall shape (e.g., rectangle, circle, triangle) and calculate its total area using the appropriate formula.

      For example:

      • For a rectangle: \text{Area} = \text{length} \times \text{width}
      • For a circle: \text{Area} = \pi r^2 where r is the radius.
      • For a triangle: \text{Area} = \frac{1}{2} \times \text{base} \times \text{height}

  2. Calculate the Area of the Shaded Region:

    • Identify the area of the shaded part of the shape. This might involve using similar formulas or subtracting smaller shapes from larger ones.

      For example:

      • If the shaded region is a smaller rectangle within a larger rectangle, find the area of the smaller rectangle using the formula for the area of a rectangle.

  3. Subtract the Area of the Shaded Region from the Total Area:

    • Once you have both the total area and the area of the shaded region, subtract the area of the shaded region from the total area to find the area of the unshaded region.

      $$ \text{Area of Unshaded Region} = \text{Total Area} - \text{Area of Shaded Region} $$

Example Problem

Let’s go through an example to illustrate this process:

Problem: Find the area of the unshaded region in a rectangle with dimensions 10 cm by 6 cm, where a smaller rectangle with dimensions 4 cm by 2 cm is shaded.

Solution:

  1. Calculate the Total Area of the Large Rectangle:

    • The dimensions of the large rectangle are 10 cm by 6 cm.
      \text{Total Area} = 10 \, \text{cm} \times 6 \, \text{cm} = 60 \, \text{cm}^2

  2. Calculate the Area of the Shaded Rectangle:

    • The dimensions of the shaded rectangle are 4 cm by 2 cm.
      \text{Area of Shaded Region} = 4 \, \text{cm} \times 2 \, \text{cm} = 8 \, \text{cm}^2

  3. Find the Area of the Unshaded Region:

    • Subtract the area of the shaded region from the total area.
      \text{Area of Unshaded Region} = 60 \, \text{cm}^2 - 8 \, \text{cm}^2 = 52 \, \text{cm}^2

Therefore, the area of the unshaded region is 52 \, \text{cm}^2.

Conclusion

By following these steps—identifying the total area, calculating the area of the shaded region, and subtracting the shaded area from the total area—you can find the area of the unshaded region for various geometric shapes. If you provide specific details about the shapes involved, I can give a more precise solution tailored to your problem.