SOLUTION: I need to solve this problem please its on this link https://drive.google.com/open?id=0B2SbxAb-ajtfZXZhZ3drcy1iUWM

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Question 1085018: I need to solve this problem please its on this link
https://drive.google.com/open?id=0B2SbxAb-ajtfZXZhZ3drcy1iUWM
Answer by ikleyn(52834) About Me  (Show Source):
You can put this solution on YOUR website!
.
The area of the rhombus is   A%5Brhombus%5D = 4%2A%28%28ab%29%2F2%29 = 2ab   (four congruent right-angled triangles).

The side length of the rhombus is   L = sqrt%28a%5E2%2Bb%5E2%29.

The perimeter of the rhombus is   4L = 4%2Asqrt%28a%5E2+%2B+b%5E2%29.

The semi-perimeter of the rhombus is   s = %284L%29%2F2 = 2%2Asqrt%28a%5E2+%2B+b%5E2%29.

The radius of the inscribed circle into the rhombus is   r = A%5Brhombus%5D%2Fs = %282ab%29%2F%282%2Asqrt%28a%5E2%2B+b%5E2%29%29 = %28ab%29%2Fsqrt%28a%5E2%2Bb%5E2%29. 

     Regarding the formula  r = A%2Fs  for the radius of inscribed circle into convex polygon, where A is the area of the polygon 
     and s is its semi-perimeter, see the lesson 
         Area of n-sided polygon circumscribed about a circle
     in this site.

Thus the area of the inscribed circle into the rhombus is  A%5Bcircle%5D = pi%2A%28%28a%5E2%2Ab%5E2%29%2F%28a%5E2+%2B+b%5E2%29%29.

Finally,  the ratio  A%5Bcircle%5D%2FA%5Brhombus%5D,  which is under the question,  is

A%5Bcircle%5D%2FA%5Brhombus%5D = %28pi%2A%28%28a%5E2%2Ab%5E2%29%2F%28a%5E2+%2B+b%5E2%29%29%29%2F%282ab%29 = %28pi%2Aa%2Ab%29%2F%282%2A%28a%5E2%2Bb%5E2%29%29.


Solved.


Also,  you have this free of charge online textbook on Geometry
    GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.


The referred lesson is the part of this online textbook under the topic "Area of polygons".