Answer:
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.
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. This depends upon the type of figure given.
What is the Area of the Shaded 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.
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.
How to Find 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.
Area of shaded region = area of outer shape – area of the unshaded inner shape
How to find the area of a shaded region in a triangle?
Let’s see a few examples below to understand how to find the area of a shaded region in a triangle.
Example 1
Calculate the area of the shaded region in the right triangle below.
Solution
Area of shaded region = area of outer shape – area of the unshaded inner shape
Area of a triangle = ½ bh.
Area of outer shape = (½ x 15 x 10) cm2.
= 75 cm2.
Area of unshaded inner shape = (½ x 12 x 5) cm2.
= 30 cm2.
Area of shaded region = (75 – 30) cm2.
= 45 cm2.
Therefore, the area of the shaded region is 45 cm2.
Example 2
Given AB = 6 m, BD = 8 m, and EC = 3 m, calculate the area of the shaded region in the diagram below.
Solution
Considering similar triangles,
AB/EC = BD/CD
6/3 = 8/CD
Cross multiply.
6 CD = 3 x 8 = 24
Divide both sides by 6.
CD = 4 m.
Now calculate the area of triangle ABD and triangle ECD
Area of triangle ABD = (½ x 6 x 8) m2
= 24 m2
Area of triangle = (½ x 3 x 4) m2
= 6 m2
Area of the shaded region = (24 – 6) m2
= 18 m2
How to find the area of a shaded region in a rectangle?
Let’s see a few examples below to understand how to find the area of the shaded region in a rectangle.
