Area of Shaded Region Calculator

The shaded region calculator helps you find the area of a square with a circle inside it. It provides accurate calculation steps and allows you to choose your preferred area unit to get results instantly.

How To Calculate Shaded Area?

Our this calculator considers the following points to determine the results:

• First of all, calculate the length of square. It can be considered as the measurement of circle diameter too
• After that, put in the value in the formula given as under:

Shaded Area Formula:

If you want to calculate the shaded area by hand, you need to subject to the following equation:

\[ \text{Shaded Area} = L^2 - \pi \left(\frac{L}{2}\right)^2 \]

Where;

L = Diameter or length of circle or square

Let us resolve an example to make your concept more clear regarding shaded area calculations!

Example: Calculating Shaded Area

Suppose we have a square with side length \(L = 53 \text{ cm}\), and we want to find the area of the shaded region (square with a circle cut out in the center).

Solution:

Step 1: Formula for the Shaded Area

The shaded area is given by: \[ \text{Shaded Area} = \text{Area of Square} - \text{Area of Circle} \]

Step 2: Express in terms of L

\[ \text{Area of Square} = L^2 \] \[ \text{Area of Circle} = \pi \left(\frac{L}{2}\right)^2 \] So, \[ \text{Shaded Area} = L^2 - \pi \left(\frac{L}{2}\right)^2 \]

Step 3: Substitute \(L = 53 \text{ cm}\)

\[ \text{Shaded Area} = 53^2 - 3.14 \left(\frac{53}{2}\right)^2 \]

Step 4: Simplify each term

\[ 53^2 = 2809 \] \[ \left(\frac{53}{2}\right)^2 = 26.5^2 = 702.25 \] \[ \pi \cdot 702.25 \approx 3.14 \cdot 702.25 = 2201.065 \]

Step 5: Calculate Shaded Area

\[ \text{Shaded Area} = 2809 - 2201.065 \approx 607.935 \text{ cm}^2 \]

So, the shaded area is approximately 608 cm².

You can also use a shaded area calculator to verify the results.

Working of Area of Shaded Region Calculator:

Let us guide you on how you can use this shaded area calculator!

Inputs:

• Enter the diameter or length of a square or circle & select its unit
• Meanwhile, select the result units as well from the very next field
• Tap Calculate

Outputs:

• Shaded area calculations in units selected

References:

From the source Wikipedia: Area, Units, Area bisectors, General formulas