Area of Shaded Region Calculator

Area of Shaded Region Calculator

Enter the diameter or length of a square or circle and select the output unit to calculate the shaded region area using this calculator.

Diameter or Length of a Square or Circle:

m ▾

Select Unit:

The advanced shaded area calculator helps you determine the shaded region of a square that contains a circle inside it. It provides accurate step-by-step calculations. Simply select your preferred area unit and get instant results within seconds.

How To Calculate Shaded Area?

Our area of shaded region calculator considers the following steps to determine the results:

First, calculate the length of the square. This value is also equal to the diameter of the circle.
Then, place the value into the formula given below.

Shaded Area Formula:

If you want to calculate the shaded area manually, use the following equation:

\(Shaded\ Area = L^{2} - \pi \times \left(\dfrac{L}{2}\right)^{2}\)

Where:

L = Diameter of the circle or length of the square

Let’s solve an example to better understand shaded area calculations.

Example:

If the length of the square is 53 cm, how do you calculate the shaded area?

Solution:

Using the shaded area formula:

\(Shaded\ Area = L^{2} - \pi \times \left(\dfrac{L}{2}\right)^{2}\)

\(Shaded\ Area = 53^{2} - 3.14 \times 26.5^{2}\)

\(Shaded\ Area = 2809 - 3.14 \times 702.25\)

\(Shaded\ Area = 2809 - 2206.1825\)

\(Shaded\ Area \approx 602.82\ cm^{2}\)

You can also use the shaded region calculator to quickly verify the above results.

Working of Area of Shaded Region Calculator:

Follow these steps to use this shaded area calculator:

Inputs:

Enter the diameter or length of the square/circle and select the unit
Select the desired output unit
Click the Calculate button

Outputs:

Shaded area in the selected units

References:

Source: Wikipedia — Area, Units, Area Bisectors, General Formulas