Question 289664
Recall that the radius is the distance from the center of the circle to the edge of the circle. So to find the radius, just find the distance from (4,8) to (5,9).



{{{d=sqrt((x[1]-x[2])^2+(y[1]-y[2])^2)}}} Start with the distance formula.



{{{d=sqrt((4-5)^2+(8-9)^2)}}} Plug in {{{x[1]=4}}},  {{{x[2]=5}}}, {{{y[1]=8}}}, and {{{y[2]=9}}}.



{{{d=sqrt((-1)^2+(8-9)^2)}}} Subtract {{{5}}} from {{{4}}} to get {{{-1}}}.



{{{d=sqrt((-1)^2+(-1)^2)}}} Subtract {{{9}}} from {{{8}}} to get {{{-1}}}.



{{{d=sqrt(1+(-1)^2)}}} Square {{{-1}}} to get {{{1}}}.



{{{d=sqrt(1+1)}}} Square {{{-1}}} to get {{{1}}}.



{{{d=sqrt(2)}}} Add {{{1}}} to {{{1}}} to get {{{2}}}.



Since  {{{d=sqrt(2)}}}, this means that {{{r=sqrt(2)}}} because the radius is the distance from the center to the edge of the circle.



{{{A=pi*r^2}}} Move onto the area of a circle formula



{{{A=pi*(sqrt(2))^2}}} Plug in {{{r=sqrt(2)}}} 



{{{A=pi*2}}} Square {{{sqrt(2)}}} to get 2.



{{{A=2pi}}} Rearrange the terms.



So the exact area is {{{A=2pi}}} which approximates to *[Tex \LARGE A \approx 6.28318531]. Round this to the nearest tenth to get *[Tex \LARGE A \approx 6.3]



So the area is approximately 6.3 square units.