Area of the Shaded Region Explanation & Examples

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. In the example mentioned, the yard is a rectangle, and the swimming pool is a circle.

Area For A Shaded Region Between An Inscribed Circle And A Square

Often, these problems and situations will deal with polygons or circles. 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. With our example yard, 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. To find the area of the shaded region of acombined geometrical shape, subtract the area of the smaller geometrical shapefrom the area of the larger geometrical shape. To find the area of shaded region, we have to subtract area of semicircle with diameter CB from area of semicircle with diameter AB and add the area of semicircle of diameter AC.

• 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.
• In the above image, if we are asked to find the area of the shaded region; we will calculate the area of the outer right angled triangle and then subtract the area of the circle from it.
• The area of a triangle is simple one-half times base times height.
• 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.

How To Find The Area Of A Shaded Region Of A Circle With An Inscribed Triangle?

We can observe that the outer rectangle has a semicircle inside it. From the figure we can observe that the forex compounding calculator diameter of the semicircle and breadth of the rectangle are common. Hence, the Area of the shaded region in this instance is 16𝝅 square units. Thus, the Area of the shaded region in this case is 72 square units. Thus, the Area of the shaded region in this example is 64 square units.

Find the Area of the Shaded Region of a Square

The unit of area is generally square units; it may be square meters or square centimeters and so on. The area of the shaded region is basically the difference between the area of the complete figure and the area of the unshaded region. For finding the area of the figures, we generally use the basic formulas of the area of that particular figure.

Solved Examples :

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. 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. See this article for further reference on how to calculate the area of a triangle. This method works for a scalene, isosceles, or equilateral triangle. In the adjoining figure, PQR is an equailateral triangleof side 14 cm.

Find the Area of the Shaded Region: Square, Rectangle, Circle and Triangle

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. Also, in an equilateral triangle, the circumcentre Tcoincides with the centroid. To find the area of shaded portion, we have to subtract area of GEHF from area of rectangle ABCD. We can observe that the outer right angled triangle has one more right angled triangle inside. Similarly , the base of the inner right angled triangle is given to be 12 cm and its height is 5 cm.

In the above image, if we are asked to find the area of the shaded region; we will calculate the area of the outer right angled triangle and then subtract the area of the circle from it. The remaining value which we get will be the area of the shaded region. 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. We can observe that the outer square has a circle inside it. From the figure we can see that the value of the side of the square is equal to the diameter of the given circle.

Read on to learn more about the Area of the Shaded Region of different shapes as well as their examples and solutions. 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.

Formula for Area of Geometric Figures :

The ways of finding the area of the shaded region may depend upon the shaded region given. For instance, if a completely shaded square is given then the area of the shaded region is the area of that square. When the dimensions of the shaded region can be taken out easily, we just have to use those in the formula to find the area of the region.

• This is a composite shape; therefore, we subdivide the diagram into shapes with area formulas.
• The side length of the four unshaded small squares is 4 cm each.
• Area is calculated in square units which may be sq.cm, sq.m.
• So, its area will be the fourth part of the area of the complete circle.
• Therefore, the Area of the shaded region is equal to 246 cm².
• The area of the shaded region is the difference between two geometrical shapes which are combined together.

There is no specific formula to find the area of the shaded region of a figure as the amount of the shaded part may vary from question to question for the same geometric figure. 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. Therefore, the Area of the Shaded Region is 28 square units.

The area of the shaded region is in simple words the area of the coloured portion in the given figure. So, the ways to find and the calculations required to find the area of the shaded region depend upon the shaded region in the given figure. These lessons help Grade 7 students learn how to find the area of shaded region involving polygons and circles. Therefore, the Area of the shaded region is equal to 246 cm². 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.

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. To find the area of shaded portion, we have to subtract area of semicircles of diameter AB and CD from the area of square ABCD.

Some of the most common are triangles, rectangles, circles, and trapezoids. Many other more complicated shapes like hexagons or pentagons can be constructed from a combination of these shapes (e.g. a regular hexagon is six triangles put together). They can have a formula for area, but sometimes it is easier to find the shapes we already recognize within them. 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. Find the area of the shaded region by subtracting the area of the small shape from the area of the larger shape.