SOLUTION: Given: A square with a quartercircle inside forming from the midpoint of one side of the square to the midpoint of another side. Question: If the area of the quartercircle is 1.

Algebra ->  Surface-area -> SOLUTION: Given: A square with a quartercircle inside forming from the midpoint of one side of the square to the midpoint of another side. Question: If the area of the quartercircle is 1.      Log On


   

Question 1046514: Given: A square with a quartercircle inside forming from the midpoint of one side of the square to the midpoint of another side.
Question: If the area of the quartercircle is 1.00, what is the area of the square?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for area of an entire circle is:
+A+=+pi%2Ar%5E2+
The formula for the area of a quarter circle is:
+A%2F4+=+%281%2F4%29%2Api%2Ar%5E2+
You are given that:
+A%2F4+=+1+
+1+=+%281%2F4%29%2Api%2Ar%5E2+
+r%5E2+=+4%2Fpi+
+r+=+2%2Fsqrt%28+pi+%29+
--------------------
+r+ is 1/2 of a side of the square,
so a side of the square is:
+s+=+4%2Fsqrt%28+pi+%29+
+A+=+s%5E2+
+A+=+16%2Fpi+
Hope I got it -check my math