# geometry What is the area of the shaded region? Mathematics Stack Exchange

Let’s see a few examples below to understand how to find the area of a shaded region in a square. Calculate the area of the shaded region in the right triangle below. 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 part can occur in two ways in polygons.

## Area of the Shaded Region – Explanation & Examples

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 https://www.1investing.in/ 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.

## How to find the area of a shaded region in a square?

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. A triangle is a three-sided polygon with three edges and vertices objectives of inflation accounting in geometry. The sum of a triangle’s internal angles equals 180 degrees, which is its most significant feature. This is also called the angle sum property of a triangle. Find the area of the shaded triangle in the figure given below.

## How To Determine the Area of a Segment of a Circle

- With our example yard, the area of a rectangle is determined by multiplying its length times its width.
- The result is the area of only the shaded region, instead of the entire large shape.
- The combination of two radii forms the sector of a circle while the arc is in between these two radii.
- Find the area of the shaded region by subtracting the area of the small shape from the area of the larger shape.
- As you saw in the section on finding the area of the segment of a circle, multiple geometrical figures presented as a whole is a problem.
- The given combined shape is combination of a circleand an equilateral triangle.

With the area of shaded region calculator, you can quickly and easily calculate the area of any shaded region. Examine an example to illustrate the method for determining the area of the shaded region within a circle. To find the area of the shaded region, square the diameter or side length and subtract the product of pi and half the side length squared. The following formula helps you to understand how to find the area of a shaded region. The calculation required to determine the area of a segment of a circle is a bit tricky, as you need to have a good grasp of finding the areas of a triangle. The picture in the previous section shows that we have a sector and a triangle.

The area of the shaded region is #1/3# of the area of the circle. 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 second way is to divide the shaded part into 3 rectangles. 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.

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. The area of a circle is pi (i.e. 3.14) times the square of the radius.

The shaded region can be located at the center of a polygon or the sides of the polygon. 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. Suppose, that the length of the square is about 45cm, so find the area of the shaded region. We can conclude that calculating the area of the shaded region depends upon the type or part of the circle that is shaded.

The remaining value which we get will be the area of the shaded region. These lessons help Grade 7 students learn how to find the area of shaded region involving polygons and circles. The area of the shaded region is most often seen in typical geometry questions.

The area of the shaded triangle given inside any polygon can be calculated using the various formulae we have outlined in the guide above. You can solve some more examples in which you have to find out the area of the shaded triangle by dividing the given polygon into more sections. This way, you will have a vast knowledge of the formulas used for finding the areas of many different shapes in geometry.

That is square meters (m2), square feet (ft2), square yards (yd2), or many other units of area measure. Firstly find the area of a smaller rectangle and then the area of the total rectangle. Calculate the shaded area of the square below if the side length of the hexagon is 6 cm.

Triangles are defined according to their angles and sides. We are given the area and the radius of the sector, so we can find the central angle of the sector by using the formula of the area of the sector. We are given the area and central angle of the sector, so we can find the radius of the sector by using the formula of the area of the sector. The area of the sector of a circle is basically the area of the arc of a circle.

Shaded triangles are provided in a variety of ways in mathematics so that their area can be calculated using an appropriate method. A triangle is a three-edged polygon having three vertices. Hopefully, this guide helped you develop the concept of how to find the area of the shaded region of the circle.