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.
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.
Find the Area of the Shaded Region – Simple and Easy Method
- The grass in a rectangular yard needs to be fertilized, and there is a circular swimming pool at one end of the yard.
- Angle in a semicircle is right angle, diameter of the circle is hypotenuse.
- The area of the shaded region is basically the difference between the area of the complete figure and the area of the unshaded region.
The area of a triangle is simple one-half times base times height. 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. Check the units of the final answer to make sure they are square units, indicating the correct units for area.
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. There are many common polygons and shapes that we might encounter in a high school math class and beyond.
The given combined shape is combination of atriangle and incircle. We will learn how to find the Area of theshaded region of combined figures. Let R be the radius of larger circle and r be the radius of smaller circle. Then add the area of all 3 rectangles to get the area of the shaded region. Then subtract the area of the smaller triangle from the total area of the rectangle.
Rectangle C
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.
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.
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.
Find the Area of the Shaded Region of a Circle
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.
How to find the area of a shaded region in a triangle?
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.
- We can observe that the outer rectangle has a semicircle inside it.
- Let’s see a few examples below to understand how to find the area of the shaded region in a rectangle.
- 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 square has a circle inside it.
Rectangle A
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.
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 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.
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.
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 forex trading reviews 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.
