So, the area of the shaded or coloured region in a figure is equal to the difference between the area of the entire figure and the area of the part that is not coloured or not shaded. Calculate the shaded area of the square below if the side length of the hexagon is 6 cm. The side length of the four unshaded small squares is 4 cm each.
Solved Examples :
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.
Find the Area of the Shaded Region – Simple and Easy Method
When dealing with shaded regions in geometry, finding their area can be a known mathematical problem. Whether it is a square, rectangle, circle, or triangle, you need to know how to find the area of the shaded region. Moreover, these Formulas come in use in different mathematical as well as real-world applications.
In such a case, we try to divide the figure into regular shapes as much as possible and then add the areas of those regular shapes. The semicircle is generally half of the circle, so its area will be half of the complete circle. Similarly, a quarter circle is the fourth part of a complete circle. So, its area will be the fourth part of the area of the complete circle. Here, the base of the outer right angled triangle is 15 cm and its height is 10 cm.
- Therefore, the Area of the shaded region is equal to 246 cm².
- 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.
- 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.
- This is a composite shape; therefore, we subdivide the diagram into shapes with area formulas.
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.
Rectangle A
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 result is the area of only the shaded region, instead of the entire large shape. In what is the forex trading secrets and tips of success 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.
We can observe that the outer rectangle has a semicircle inside it. From the figure we can observe that the 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.
Worksheet on Construction of Triangles Constructing Triangles Math
That is square meters (m2), square feet (ft2), square yards (yd2), or many other units of area measure. The given combined shape is combination of a circleand an equilateral triangle. Angle in a semicircle is right angle, diameter of the circle is hypotenuse. By drawing the horizontal line, we get the shapes square and rectangle. Area is calculated in square units which may be sq.cm, sq.m.
Find the Area of the Shaded Region: Square, Rectangle, Circle and Triangle
In a given geometric figure if some part of the figure is coloured or shaded, then the area of that part of figure is said to be the area of the shaded region. There are three steps to find the area of the shaded region. Subtract the area of the inner region from the outer region. Calculate the area of the shaded region in the diagram below. Calculate the area of the shaded region in the right triangle below.
Find the Area of the Shaded Region of a Circle
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.
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.
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.
- So, its area will be the fourth part of the area of the complete circle.
- So, the area of the shaded or coloured region in a figure is equal to the difference between the area of the entire figure and the area of the part that is not coloured or not shaded.
- We can observe that the outer rectangle has a semicircle inside it.
- We can observe that the outer square has a circle inside it.
- Area is calculated in square units which may be sq.cm, sq.m.
Area of the smaller rectangle
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.