How to Calculate the Area of Shaded Regions

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The grass in a rectangular yard needs to be fertilized, and there is a circular swimming pool at one end of the yard. The amount of fertilizer you need to purchase is based on the area needing to be fertilized. So, what area of the yard needs to be fertilized? This question can be answered by learning to calculate the area of shaded regions. In this type of problem, the area of a small shape is subtracted from the area of a larger shape that surrounds it. The area outside the small shape is shaded to indicate the area of interest.

    Determine what basic shapes are represented in the problem. Each shape must have its own area equation. In the example mentioned, the yard is a rectangle, and the swimming pool is a circle.

    Calculate the area of both shapes. The area of a rectangle is determined by multiplying its length times its width. The area of a circle is Pi (i.e., 3.14) times the square of the radius.

    Find the area of the shaded region by subtracting the area of the small shape from the area of the larger shape. The result is the area of only the shaded region, instead of the entire large shape. In this example, the area of the circle is subtracted from the area of the larger rectangle.

    Check the units of the final answer to make sure they are squared, indicating the correct units for area.

    Tips

    • Problems that ask for the area of shaded regions can include any combination of basic shapes, such as circles within triangles, triangles within squares, or squares within rectangles.

      Sometimes either or both of the shapes represented are too complicated to use basic area equations, such as an L-shape. In this case, break the shape down even further into recognizable shapes. For example, an L-shape could be broken down into two rectangles. Then add the two areas together to get the total area of the shape.

References

About the Author

Joshua Bush has been writing from Charlottesville, Va., since 2006, specializing in science and culture. He has authored several articles in peer-reviewed science journals in the field of tissue engineering. Bush holds a Ph.D. in chemical engineering from Texas A&M University.

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