How To Find The Area of a circle drawn inside a square


So far at this site you have learned how to find the area of a circle using its radius, diameter and circumference. Now is the best time to apply this knowledge on other types of math problems involving area of circles.


Going in this direction, the first type of problems can be on finding the area of a circle drawn inside a square of given side length. It can be other way around too. That is, finding the area of a square having a circle drawn inside it with given area.


Today’s presentation is to explore finding the area of a circle drawn inside a square with known side length. Below is the step by step explanation to approach such type of problems. Follow these steps whenever you have to find the area of a circle inscribed in a square. Must read the whole presentation to get perfect on the topic.


The steps to find the area of a circle inscribed inside a square of given length:

 

  • Write down the side length of the square.
  • The side length of the square is also equal to the diameter of the circle, hence write the diameter of the circle equal to the side length of the square.
  • Half the diameter is radius, so divide the side length by 2 to get the radius “r” of the circle.
  • Once you know the radius of the circle, find its area using formula for area of a circle  Area of a circle formula.


Now let's apply the above information on a concrete example on this topic. Look at the diagram given below, asking to find the circle area inside a square of a side length of 12 inches.


How to find the area of a circle inside a square


Circle Drawn Inside A Square





So let's apply these steps to find the area of the circle given in the above problem


Given side length of the square = 12'


Diameter of the circle = Side length of the square = 12'


Radius of the circle = Diameter 2 = 12 2 = 6'


Now area of the circle " A" = pi x radius x radius = 3.14 x 62  = 3.13 x 36 = 113.04 square inches



Finding the area between the circle and the square:


But there is another question in the given problem asking us to find the area between the circle and the square boundaries (this is the green shaded area in the diagram).

To do this; follow the given steps below:


  • Find the area of the square by squaring its sides (side x side).
  • Take away the area of the circle calculated above from area of the square to find the area between the  circle and square.
  •  

So, let's find the shaded area between the circle and square boundaries.


Side length of square "s" = 12 inches


Area of the square = s x s = 12 x 12 = 144 square inches or 144 sq.inch 


Hence the shaded area = Area of the square - The area of the circle

                                     = 144 - 113.04 = 30.96 sq.in


Finally we wrap up the topic of finding the area of a circle drawn inside a square of a given side length. You also learned how to find the area of region between the circle and the square boundaries.


Now apply this knowledge in your math learning related to area of a circle geometry.


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