# 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?

Aug 23, 2015

=color(blue)(45.82m^2

#### Explanation:

The area of the plot (square) = $36 {m}^{2}$ so the side of the square
$= \sqrt{36} = 6 m$

So the perimeter that the fence covers = $4 \cdot s i \mathrm{de} = 4 \cdot 6 = 24 m$

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

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

$2 \pi r = 24 m$
$2 \times 3.14 \times r = 24$
$r = \frac{24}{6.28}$
$r = 3.82 m$

Now that we have the radius we can find the area of the circular plot:
area $= \pi \times {r}^{2}$
$= 3.14 \times {3.82}^{2}$
=color(blue)(45.82m^2