Question 561542
Joey has his dog on a leash tied on the corner of the garage. The garage is 20 feet by 30 feet. If the leash is 24 feet long, how much area can the dog access?
<pre>
{{{drawing(400,2500/7,-25,31,-25,25,locate(-2,23,4),
locate(.5,12,20), locate(12,0,24), locate(27,0,6),
rectangle(0,0,30,20),red(arc(0,0,48,-48,90,360)), green(arc(0,20,8,-8,0,90), line(0,20,0,24)) )}}}

This is the red {{{3/4}}}ths of a 24ft-radius circle plus 
{{{1/4}}} of a 4ft-radius circle.

The area of a full circle is A = <font face = "symbol">p</font>r².

The area of the big red {{{3/4}}} circle = {{{3/4}}}<font face="symbol">p</font>r².
 
=  {{{3/4}}}<font face="symbol">p</font>·r² = {{{3/4}}}·(3.14)·(24)².

The area of the small green {{{1/4}}} circle = {{{1/4}}}<font face="symbol">p</font>r².
 
=  {{{1/4}}}<font face="symbol">p</font>·r² = {{{1/4}}}·(3.14)·(4)².


Total area = {{{3/4}}}·(3.14)·(24)² + {{{1/4}}}·(3.14)·(4)².

Total area = 1356.48 + 12.56 = 1369.04 square feet.

Edwin</pre>