Given the side of a square. The task is to find the area of an inscribed circle in a square.
Input : a = 8 Output : Area of an inscribed circle: 50.24 Input : a = 12.04 Output : Area of an inscribed circle: 113.795
Given a square i.e. all sides of a square are of equal length and all four angles are 90 degrees. Below diagram depicts an inscribed circle in a square.
Properties of an inscribed circle in a square:
- The diameter of an inscribed circle in a square is equal to the length of the side of a square.
- With at least one measure of the circle or the square, the area and the perimeter of the square can be calculated in which the circle is inscribed.
- The center of the square and the center of the circle lie at a same point.
- when at least one measure of the circle or the square is given, the circumference and area of the circle can be calculated.
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- Area of a circle inscribed in a regular hexagon
- Area of circle which is inscribed in equilateral triangle
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- Find area of the larger circle when radius of the smaller circle and difference in the area is given
- Radius of the biggest possible circle inscribed in rhombus which in turn is inscribed in a rectangle
- Program to find the side of the Octagon inscribed within the square
Formula to find the area of an inscribed circle:
where a is the side of a square in which a circle is inscribed.
How does the formula works?
Assume a is the side of a square and we know that a square has 4 sides.
Area of a circle =
where r is the radius of a circle and area of a square = a2
Therefore, the area of an inscribed circle in a square =
Now, put r = a / 2
So, the area of an inscribed circle in a square =
Area of an inscribed circle:50.24
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Improved By : vt_m