Answer:
(a)2(89x+84)
(b)[tex]2(89x+84-x^2\pi)[/tex]
Step-by-step explanation:
The dimensions of the larger rectangular field are:
The dimensions of the smaller rectangular soccer field are:
(a)Area of the part of the field that is outside the soccer field
=Area of the larger rectangular field - Area of the Soccer Field
=(5x+12)(9x+14)-5x(9x)
=(5x)(9x)+70x+108x+168-5x(9x)
=178x+168
=2(89x+84)
(b)Radius of the Semicircular Fountain =2x
From Part (a),
Area of the larger rectangular field - Area of the Soccer Field=178x+168
Area of the Semicircular Fountain =[tex]\dfrac{\pi r^2}{2} =\dfrac{\pi (2x)^2}{2} =\dfrac{4x^2\pi}{2} =2x^2\pi[/tex]
Area of the Field that does not include the soccer field or the fountain.
=Area of the larger rectangular field - Area of the Soccer Field-Area of the Semicircular Fountain
[tex]=178x+168-2x^2\pi\\=2(89x+84-x^2\pi)[/tex]
