The area of the shaded region a = πr² - (2r)² has been proved
How to prove the area of the shaded region
From the question, we have the following parameters that can be used in our computation:
The inscribed square in a circle
Where, we have
Radius of circle = r
The area of a circle is calculated as
Circle area = πr²
For the square, we have the side length to be
L = 2 * radius of circle
So, we have
L = 2r
The area of a square is
Area = L²
So, we have
Area = (2r)²
The shaded region is then calculated as
Shaded region, a = Circle area - Square area
Substitute the known values into the equation
a = πr² - (2r)²
Hence, the area of the shaded region has been proved
Question
A square fits exactly inside a circle of radius r, as shown. a is the area of the shaded region.
show that a = πr² - (2r)²