Question 712322
What you mean is half of the space between two concentric circles,
the inner one with a 6-foot radius,
and the outer one with an 8-foot radius:
{{{drawing(300,200, -9,9,-2,10,
green(line(-9,0,9,0)),blue(circle(0,0,6)),red(circle(0,0,8)),
locate(-7.2,1,2),locate(-3.2,1,6),
locate(2.8,1,6),locate(6.8,1,2),
green(line(0,-0.2,0,0.2)),locate(3,2.9,red(8)),
red(arrow(2.8,2.1,0.1,0.1)),red(arrow(3.6,2.7,6.4,4.8)),
locate(-2,2.9,blue(6)),
blue(arrow(-1.5,2,-0.1,0.1)),blue(arrow(-2.1,2.8,-3.6,4.8))
)}}} The surface area of the space bounded by the two circles (red and blue),
and the (green) line that splits the circles is calculated to about 43.96,
when using {{{pi=3.14}}}.
The surface area of the whole outer circle (in square feet) is
{{{pi*8^2}}} and half of that is {{{pi*8^2/2}}}
The surface area of the whole inner circle (in square feet) is
{{{pi*6^2}}} and half of that is {{{pi*6^2/2}}}
The area we want to calculate (in square feet) is
{{{pi*8^2/2-pi*6^2/2}}} or {{{(pi*8^2-pi*6^2)/2}}}
{{{(pi*8^2-pi*6^2)/2=(64pi-36pi)/2=28pi/2=highlight(14pi)}}}
{{{14*3.14=highlight(43.96)}}} which is accurate enough.
Using {{{pi=3.1416}}} we get {{{14*3.1416=43.9824,
and with a calculator that uses a much more accurate value for {{{pi}}}
we get
{{{14pi=about43.9823}}}