Answer:
Area of the rectangle(A) is given by:
[tex]A = lw[/tex]
where,
l is the length and w is the width of the rectangle respectively.
As per the statement:
The yard is rectangular and measures 10x by 15x
⇒[tex]\text{Area of rectangular yard}=10x \cdot 15x = 150x^2[/tex]
It is also given that:
the fountain is going to be circular with a radius of 4x.
Area of a circle(A') is given by:
[tex]A' = \pi r^2[/tex] where, r is the radius of the circle.
Use [tex]\pi = 3.14[/tex]
then;
[tex]\text{Area of a circular fountain} = \pi (4x)^2 = 16x^2 \cdot 3.14 = 50.24x^2[/tex]
We have to find the he area of the remaining yard.
[tex]\text{Area of the remaining yard} = \text{Area of the rectangular yard} - \text{Area of a circular fountain}[/tex]
Substitute the given values we have;
[tex]\text{Area of the remaining yard} = 150 x^2-50.24x^2 = 99.76 x^2[/tex]
Therefore, the area of the remaining yard will be, [tex]99.76 x^2[/tex]
