# Find the Area of the Shaded Region: Square, Rectangle, Circle and Triangle

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. Read on to learn more about the Area of the Shaded Region of different shapes as well as their examples and solutions.

## What is the Formula for the Area of the Shaded Region?

The formula for finding the Area of a Shaded region depends on the shape of the region. Moreover, here are the basic formulas for some common geometric shapes:

Square:

Area of Shaded Region=Area of Square−Area of Inscribed Shape

Rectangle:

Area of Shaded Region=Area of Rectangle−Area of Inscribed Shape

Circle:

Area of Shaded Region=Area of Circle−Area of Inscribed Shape

Triangle:

Area of Shaded Region=Area of Triangle−Area of Inscribed Shape

Also Read: Area and Perimeter Questions

## How to find the Area of the Shaded Region?

Additionally, to calculate the area of the Shaded region accurately, you will need to follow these steps:

• Identify the Shapes: Determine the shapes in the problem, such as squares, rectangles, circles, or triangles.
• Calculate Individual Areas: Find the area of each shape using the appropriate formulas.
• Subtract Areas: Subtract the area of the smaller shape from the area of the larger shape to Find the Area of the Shaded region.

## Find the Area of the Shaded Region of a Square

Consider a Square with a side length of 10 units. Inside this square, there is another smaller square inscribed with a side length of 6 units. To Find the Area of the Shaded Region:

1. Calculate Areas:
• Area of Larger Square = 10×10=100 square units.
• Area of Smaller Square = 6×6=36 square units.
1. Subtract Areas:
• Area of Shaded Region = 100−36=64 square units.

Thus, the Area of the shaded region in this example is 64 square units.

## Find the Area of the Shaded Region of a Rectangle

Suppose we have a Rectangle with dimensions 12 units by 8 units. Inside this rectangle, there is another smaller rectangle with dimensions 6 units by 4 units. To Find the Area of the Shaded Region:

1. Calculate Areas:
• Area of Larger Rectangle = 12×8=96 square units.
• Area of Smaller Rectangle = 6×4=24 square units.
1. Subtract Areas:
• Area of Shaded Region = 96−24=72 square units.

Thus, the Area of the shaded region in this case is 72 square units.

## Find the Area of the Shaded Region of a Circle

Imagine a Circle with a radius of 5 units. Inside this circle, there is another smaller circle with a radius of 3 units. To Find the Area of the Shaded region:

1. Calculate Areas:
• Area of a Larger Circle = 𝝅 ✕ 5= 25𝝅 square units (using the formula 𝝅r2 ).
• Area of Smaller Circle = 𝝅 ✕ 3= 9𝝅 square units.
1. Subtract Areas:
• Area of Shaded Region = 25𝝅 – 9𝝅 = 16𝝅 square units.

Hence, the Area of the shaded region in this instance is 16𝝅 square units.

## Find the Area of the Shaded Region of a Triangle

Consider a Triangle with a base of 10 units and a height of 8 units. Inside this triangle, there is another smaller triangle with a base of 6 units and a height of 4 units. To calculate the Area of the shaded region:

1. Calculate Areas:
• Area of Larger Triangle = ½ ✕ 10 ✕ 8 = 40 square units.
• Area of Smaller Triangle = ½ ✕ 6 ✕ 4 = 12 square units.
1. Subtract Areas:
• Area of Shaded Region = 40 – 12 = 28 square units.

Therefore, the Area of the Shaded Region is 28 square units.