probability of geometric figures

Question

i have a square with a circle inside it. measurement on the outside are length 20cm  width 20cm what is the probability that a dart will land in the shaded region.. the circle is the shaded region

 

Answer 1

I assume the circle is inscribed within the square; that is, it just touches each side of the square.  In that case, the circle's radius is (1/2)*(20) = 10 cm.  The area of the circle is:

 

A_C = pi*radius² = (3.14)*(10²) = 314 cm²

 

The area of the square is:

 

A_S = (side)² = 20² = 400 cm²

 

The probability that a dart will land within the circle (if it lands within the square) is:

 

A_C/A_S = 314/400 = 0.785