Sometimes, you may be required to calculate the area of shaded regions. Usually, we would subtract
the area of a smaller inner shape from the area of a larger outer shape in order to find the area
of the shaded region. If any of the shapes is a composite shape then we would need to subdivide it
into shapes that we have area formulas, like the examples below. Hopefully, this guide helped you develop the concept of how to find the area of the shaded region of the circle. 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. 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. 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 data warehouse terms total area of the entire polygon. 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.
- Then subtract the area of the smaller triangle from the total area of the rectangle.
- Our usual strategy when presented with complex geometric shapes is to partition them into simpler shapes whose areas are given by formulas we know.
- The area of the circular shaded region can also be determined if we are only given the diameter of the circle by replacing “$r$” with “$2r$”.
- For more difficult
questions, the child may be encouraged to work out the problem on a piece of paper
before entering the solution.
Two circles, with radii 2 and 1 respectively, are externally tangent (that is, they intersect at exactly one point). The following diagram gives an example of how to find the area of a shaded region. These lessons help Grade 7 students learn how to find the area of shaded region involving polygons and circles.
Area of Shaded Region Worksheet (rectangles and triangles)
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. 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.
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. In today’s lesson, we will use the strategy of calculating the area of a large shape and the area of the smaller shapes it encloses to find the area of the shaded region between them. Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
Area of the Shaded Region
Subtract the area of the white space from the area of the entire rectangle. To find the area of a rectangle, multiply its height by its width. For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area. 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.
What is the Area of the Shaded Region ?
So finding the area of the shaded region of the circle is relatively easy. All you have to do is distinguish which portion or region of the circle is shaded and apply the formulas accordingly to determine the area of the shaded region. Find the area of the shaded region in terms of pi for the figure given below. Afterwards, we can solve for the radius and central angle of the circle. This is a composite shape; therefore, we subdivide the diagram into shapes with area formulas.
How to find the area of the shaded region using the area?
Then subtract the area of the smaller triangle from the total area of the rectangle. We are given the arc length of the circle and an arc length is a fraction/part of the circumference of the circle. 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.
To find the area of the shaded region of a
combined geometrical shape, subtract the area of the smaller geometrical shape
from the area of the larger geometrical shape. The general rule to find the shaded area of any shape would be to subtract the area of the more significant portion from the area of the smaller portion of the given geometrical shape. Still, in the case of a circle, the shaded area of the circle can be an arc or a segment, and the calculation is different for both cases. The shaded region can be located at the center of a polygon or the sides of the polygon.
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. 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 https://traderoom.info/ the shaded region depend upon the shaded region in the given figure. 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. We can observe that the outer rectangle has a semicircle inside it.
The formula to determine the area of the shaded segment of the circle can be written as radians or degrees. The area of the sector of a circle is basically the area of the arc of a circle. The combination of two radii forms the sector of a circle while the arc is in between these two radii. To find the area of the shaded region of a circle, we need to know the type of area that is shaded.
From the figure we can observe that the diameter of the semicircle and breadth of the rectangle are common. The given combined shape is combination of a circle
and an equilateral triangle. Our usual strategy when presented with complex geometric shapes is to partition them into simpler shapes whose areas are given by formulas we know.
