Shaded Area Calculator
How to find the area of a shaded region? This tool can makes this easy for you. Simple enter specific values diameter or length into the calculator, you can quickly determine the shaded area between a square and a circle.
What is Shaded Area?
The shaded area mean the space that is covered between a larger square and a smaller circle within it. This area can be important in various fields, including architecture and design.
Calculating the Shaded Area of a Square with Inscribed Circle
Imagine a square. Now, draw the largest circle you can inside that square. The space between the circle’s edge and the square’s side is the shaded area.
Using the Calculator
To find this shaded area, simply:
- Enter the diameter or side length of the square. This is the distance across the square.
- Click “Calculate.”
The Formula Behind the Magic
The formula used to calculate the shaded area is:
Shaded Area = Area of Square – Area of Circle
- Area of Square = side²
- Area of Circle = π × (radius)²
Let’s do an example:
If the side of the square is 10 units:
-
Find the area of the square:
- Area of square = 10² = 100 square units
-
Find the radius of the circle:
- The diameter of the circle is equal to the side of the square.
- So, the radius is half the side length: 10 / 2 = 5 units
-
Find the area of the circle:
- Area of circle = π × 5² ≈ 78.54 square units
-
Calculate the shaded area:
- Shaded area = 100 – 78.54 ≈ 21.46 square units
Why is this useful?
Understanding this concept can help in various fields, from engineering to art and design. It’s a fundamental problem in geometry that has real-world applications.
So, next time you see a square with a circle inside, you’ll know how to calculate the shaded area!
