Question

Will fan and medal. How is this correct?

Answer 1

Step $1$

Find the area of the rectangular yard

the area of the rectangular yard is equal to

$A=L*W$

where

L is the length side of the rectangle

W is width side of the rectangle

in this problem we have

$L=7x\ units\\W=6x\ units$

$A=L*W$

$A=7x*6x$

$A=42x^{2}\ units^{2}$

Step $2$

Find the area of a circular fountain

we know that

the area of a circle is equal to

$A=\pi r^{2}$

where

r is the radius of the circle

in this problem we have

$r=2x\ units$

substitute

$A=\pi (2x)^{2}$

$A=4\pi x^{2}\ units^{2}$

Step $3$

Find area of the remaining yard

Subtract the area of a circular fountain from the area of the rectangular yard

$42x^{2}\ units^{2}-4 \pi x^{2}\ units^{2}=2x^{2}[21-2\pi]$

therefore

the answer is the option B

$2x^{2}[21-2\pi]\ units^{2}$

Answer 2

The yard is rectangular with a measurement of 7x by 6x. 
The fountain is circular with a radius of 2x.
Since we are looking for the remaining area, we need to know the area of the rectangular backyard and the circular fountain.

The formula for a rectangle is 
A=lw
where:
 l=length
 w=width 

So, 
A=(7x)(6x)
  =42x^2

Now for the area of the circular fountain, 
A=