Question

A farmer has a fence that encloses a square plot with an area of 36 sq. m. If the farmer uses this fence to enclose a circular flower garden, what will the area of the garden be?

Answer 1

`=color(blue)(45.82m^2`

Explanation:

The area of the plot (square) = `36m^2` so the side of the square
`=sqrt36 = 6m`

So the perimeter that the fence covers = `4*side = 4*6 = 24m`

This value is basically the entire length of the fence used.

Now since the same `24m` is used to fence a circular area , the perimeter of the circular area can be equated to `24m`

`2pir=24m`
`2 xx 3.14 xx r=24`
`r=24/6.28`
`r=3.82m`

Now that we have the radius we can find the area of the circular plot:
area `=pi xx r^2`
`=3.14 xx 3.82^2`
`=color(blue)(45.82m^2`