Then add the area of all 3 rectangles to get the area of the shaded region. In this problem, it is easy to find the area of the two inner circles, since their radii are given. We can also find the area of the outer circle when we realize that its diameter is equal to the sum of the diameters of the two inner circles. Try the free Mathway calculator andproblem solver below to practice various math topics. Try the given examples, or type in your ownproblem and check your answer with the step-by-step explanations.

Sometimes, you may be required to calculate the area of shaded regions. Usually, we would subtractthe area of a smaller inner shape from the area of a larger outer shape in order to find the areaof the shaded region. If any of the shapes is a composite shape then we would need to subdivide itinto shapes that we have area formulas, like the examples below. The area of the shaded region is the difference between two geometrical shapes which are combined together. By subtracting the area of the smaller geometrical shape from the area of the larger geometrical shape, we will get the area of the shaded region. Or subtract the area of the unshaded region from the area of the entire region that is also called an area of the shaded region.

The area of the shaded part can occur in two ways in polygons. The shaded region can be located at the center of a polygon or the sides of the polygon. It is also helpful to realize that as a square is a special type of rectangle, it uses the same formula to find the area of a square. The area of a triangle is simple one-half times base times height. Check the units of the final answer to make sure they are square units, indicating the correct units for area. That is square meters (m2), square feet (ft2), square yards (yd2), or many other units of area measure.

## Finding The Area Of The Shaded Region Step-By-Step (2 Different Ways)

Or we can say that, to find the area of the shaded region, you have to subtract the area of the unshaded region from the total area of the entire polygon. Our usual strategy when presented with complex geometric shapes is to partition them into simpler shapes whose areas are given by formulas we know. Two circles, with radii 2 and 1 respectively, are externally tangent (that is, they intersect at exactly one point). Sometimes we are presented with a geometry problem that requires us to find the area of an irregular shape which can’t easily be partitioned into simple shapes. So, the Area of the shaded region is equal to 317 cm². Therefore, the Area of the shaded region is equal to 246 cm².

The side length of the four unshaded small squares is 4 cm each.

## Sciencing_Icons_Solutions Solutions

There are three steps to find the area of the shaded region. Subtract the area of the inner region from the outer region. Let’s see a few examples below to understand how to find the area of a shaded region in a square. This is a composite shape; therefore, we subdivide the diagram into shapes with area formulas. Let’s see a few examples below to understand how to find the area of the shaded region in a rectangle. Let’s see a few examples below to understand how to find the area of a shaded region in a triangle.

- That is square meters (m2), square feet (ft2), square yards (yd2), or many other units of area measure.
- Check the units of the final answer to make sure they are square units, indicating the correct units for area.
- It is also helpful to realize that as a square is a special type of rectangle, it uses the same formula to find the area of a square.
- The area of the shaded region is the difference between the area of the entire polygon and the area of the unshaded part inside the polygon.

Therefore, the Area of the shaded region is equal to 16cm². The following diagram gives an example of how to find the area of a shaded region. The area of the shaded region is most often seen in typical geometry questions. Such questions always have a minimum of two shapes, for which you need to find the area and find the shaded region by subtracting the smaller area from the bigger area.

## Area Of Shaded Region

Determine what basic shapes are represented in the problem. In the example mentioned, the yard is a rectangle, and the swimming pool is a circle. Often, these problems and situations will deal with polygons or circles.

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. With our example yard, the area of a rectangle is determined by multiplying its length times its width.

Calculate the area of the shaded region in the diagram below. Calculate the area of the shaded region in the right triangle below. Then subtract the area of the smaller triangle from the total area of the rectangle. Follow the below https://www.dowjonesrisk.com/ steps and know the process to find out the Area of the Shaded Region. We have given clear details along with the solved examples below. Calculate the shaded area of the square below if the side length of the hexagon is 6 cm.

There are many common polygons and shapes that we might encounter in a high school math class and beyond. Some of the most common are triangles, rectangles, circles, and trapezoids. They can have a formula for area, but sometimes it is easier to find the shapes we already recognize within them.

But in this case, and in many similar geometry problems where the shape is formed by intersecting curves rather than straight lines, it is very difficult to do so. Some examples involving the area of triangles and circles. Also, some examples to find the area of ashaded region. These lessons help Grade 7 students learn how to find the area of shaded region involving polygons and circles. As stated before, the area of the shaded region is calculated by taking the difference between the area of an entire polygon and the area of the unshaded region. The area of the shaded region is the difference between the area of the entire polygon and the area of the unshaded part inside the polygon.

## Rectangle A

The area of a circle is pi (i.e. 3.14) times the square of the radius. 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. This question can be answered by learning to calculate the area of a shaded region. 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.