Question

1. A family is building a circular fountain in the backyard. The yard is rectangular and measures 10x by 15x and the fountain is going to be circular with a radius of 4x. Once the fountain is built, what will be the area of the remaining yard?
2. A sports team is building a new stadium on a rectangular lot of land. The lot measures 8x by 12x and the field will be 3x by 6x. How much land will be left for the bleachers, restrooms, and other parts of the stadium?

Answer 1

1. The remaing area of the yard will be found as follows:
Area of the yard

A1=length*width=10x*15x=150x^2 yd^2

area of the fountain
A2=πr²
A2=π(4x)²
=50.266x^2

The remaining area will be:
A=150x^2-50.266x^2
A=99.735x^2 yd^2


2] Area left for bleachers, restrooms and other parts of the stadium will be as follows:
Area of the lot is:
A1=length*width
A1=8x×12x= 96x^2 

Area of the field
A2=length×width
A2=3x×6x=18x^2

Hence the remaining area will be:
A1-A2
=96x^2-18x^2
=78x^2 sq. units