SOLUTION: There is a diagram with a square inside a circle. The circle is shaded in, but the square isnt. You have to find the area of the shaded region. The only information given is that t

Algebra ->  Algebra  -> Surface-area -> SOLUTION: There is a diagram with a square inside a circle. The circle is shaded in, but the square isnt. You have to find the area of the shaded region. The only information given is that t      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 188033: There is a diagram with a square inside a circle. The circle is shaded in, but the square isnt. You have to find the area of the shaded region. The only information given is that the square has a base and a height of 4. How do you do that?
Answer by Alan3354(21600) About Me  (Show Source):
You can put this solution on YOUR website!
There is a diagram with a square inside a circle. The circle is shaded in, but the square isnt. You have to find the area of the shaded region. The only information given is that the square has a base and a height of 4. How do you do that?
-------------------
The area of the shaded region is the area of the circle minus the area of the square.
The area of the square = 4*4 = 16 sq units.
The diameter of the circle is the diagonal of the square. Using Pythagoras:
d%5E2+=+4%5E2+%2B+4%5E2
d+=+sqrt%2832%29
r+=+sqrt%2832%29%2F2
Area of the circle = pi%2Ar%5E2
AC = pi*32/4 = 8pi
Shaded region = 8pi - 16
= ~ 9.1327 sq units