Question 920327

area of the circle is {{{A=pi*r^2}}} where {{{r=radius}}}

 you also know that diameter {{{D=2r}}}; consequently,{{{D^2=(2r)^2=4r^2}}}
	  	
so, when you know the {{{diameter}}} and want to use it to find area, then you have to express {{{r^2}}} in terms of {{{D^2}}}:

{{{D^2=4r^2}}}=>{{{r^2=D^2/4}}} or {{{r^2=(1/4)D^2}}}

then go to {{{A=pi*r^2}}} and substitute {{{(1/4)D^2}}} for {{{r^2}}}

{{{A=pi*(1/4)D^2}}}

{{{A = (pi/4)*D^2}}}