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Sticky Note
Circumference of circle = perimeter of square. Circle area is?
  1. Equal
  2. Less than
  3. Greater than
  4. None of these
Explanation

Let the circumference of the circle = perimeter of the square = P  

- Circumference of circle = 2πr  

- Perimeter of square = 4a (a = side of square)  


So, 2πr = 4a ⇒ a = (πr)/2


- Area of circle = πr²  

- Area of square = a² = (πr/2)² = (π²r²)/4


Now compare:

πr² (circle) vs. (π²r²)/4 (square)  

Divide both sides:  

(πr²) / ((π²r²)/4) = 4/π > 1 ⇒ area of circle > area of square.


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