Question

A garden, shaded in the diagram below,

consists of four quarter-circles of equal
size inside a square. The landscaper
decides to put a fence around both the
inside and the outside of the garden....

How much fencing, in yards, will the landscaper need for the fence?

Answer 1

Check the picture below.

so let's notice, since the garden is using four quarters, well, four quarters of anything is a whole anything, so if we add them all together that'd give us a full circle whose radius is 5 yards.

So the perimeter of the garden and thus its fencing including the straight border outside is simply the circumference of the circle and the perimeter of the square

`\stackrel{ \textit{\LARGE perimeters} }{\stackrel{ circle }{2\pi (5)}~~ + ~~\stackrel{ square }{4(10)}}\implies 10\pi +40 ~~ \approx ~~ \text{\LARGE 71.42}~yards`