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Find the area of a circle inscribed in a square of side 28 cm as shown in figure.
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Last updated date: 13th Jun 2024
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Answer
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Hint: When a circle is inscribed in a square the diameter of the circle is equal to the side length of the square.
You can find the perimeter and area of the square, when at least one measure of the circle or the square is given.
For a square with side length S, the following formulas are used
Perimeter \[ = 4S\]
Area \[ = {S^2}\]
Diagonal \[ = S\sqrt 2 \]
For a circle write the radius r, the following formulas are used circumference \[ = 2\pi r\]
Area \[ = \pi {r^2}\]
Therefore,

Complete step-by-step answer:
As we know before the diameter of the circle is equal to the side length of the square.
The side length of the square \[ = 28\,cm\]
Area of a circle \[ = \pi {r^2}\]
To find the area first of all we find the radius of the circle.
\[d = 28\,cm\, = \]side length of the square
Where ‘d’ is diameter of the circle
\[r = \dfrac{d}{2} = \dfrac{{28}}{2} = 14\,cm\]
As we know that radius is half of the diameter
Now we have the value of ‘r’ that is 14 cm
Putting the value of r in the formula
Area of circle
\[ = \pi {r^2}\]
\[ = \pi \times {(14)^{2\,}}\,c{m^2}\]
\[ = 196\,\pi \,c{m^2}\]
Hence the area of the circle is \[196\,\pi \,c{m^2}\]

Note: If they ask to find the area of the square, we used the formula
Area of the square \[ = {S^2}\]
\[S = 28\,cm\]
\[ = 28 \times 28\,c{m^2}\]
\[ = 784\,c{m^2}\]