Question 1158724


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 

{{{(3sqrt( 2) )^2=r^2+r^2}}}

{{{2r^2=9*2}}}

{{{r^2=9}}}

{{{r=3}}}

the area of circle is: {{{r^2*pi}}}= {{{9*pi}}}≈{{{28.27}}}

the area of triangle: {{{(1/2)r^2=9/2=4.5}}}

shaded area= {{{1/4}}} of circle area {{{minus}}} triangle area

{{{1/4}}} of circle area  is {{{(1/4)28.27=7.07}}}

shaded area={{{ 7.07-4.5}}}≈{{{2.57}}}