SOLUTION: Given circles Z with XY=3 radical 2. Find the area of the shaded region. https://docs.google.com/document/d/13qS6BeAbLGXOx7DAzfLBVsfPuzSViSurw4ynTJtS7bE/edit Thank you!

Algebra ->  Circles -> SOLUTION: Given circles Z with XY=3 radical 2. Find the area of the shaded region. https://docs.google.com/document/d/13qS6BeAbLGXOx7DAzfLBVsfPuzSViSurw4ynTJtS7bE/edit Thank you!      Log On


   

Question 1158724: Given circles Z with XY=3 radical 2. Find the area of the shaded region.
https://docs.google.com/document/d/13qS6BeAbLGXOx7DAzfLBVsfPuzSViSurw4ynTJtS7bE/edit
Thank you!
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Given circles Z with XY=3sqrt( 2)
Find the area of the shaded region.


central angle 90°-> triangle XZY is right triangle with congruent legs, each equal to radius r
XY+is hypotenuse, so
%283sqrt%28+2%29+%29%5E2=r%5E2%2Br%5E2
2r%5E2=9%2A2
r%5E2=9
r=3
the area of circle is: r%5E2%2Api= 9%2Api≈28.27
the area of triangle: %281%2F2%29r%5E2=9%2F2=4.5
shaded area= 1%2F4 of circle area minus triangle area
1%2F4 of circle area is %281%2F4%2928.27=7.07
shaded area=+7.07-4.5≈2.57