Answer :
Answer:
Square side=40ft
Semi-circle diameter=39.98ft
Area of court=2276.69 ft^2
Step-by-step explanation:
The square section has a semicircle joined to it and the combined perimeter is 182.8 ft.
-Area of the square section is obtained by subtracting that of the semicircle from the total(only 3 sides of the square is used since one side is attached to the semi-circle)
[tex]A_T=A_{sc}+A_{sq}\\\\=\frac{1}{2}\pi D+3s\\\\=182.8=62.8+3s\\\\s=40\ ft[/tex]
Hence, the square's sides has the dimension of 40 ft.
The semi-circle's diameter is calculated as:
[tex]P=\frac{1}{2}\pi D\\\\62.8=0.5\pi D\\\\D=\frac{62.8}{0.5\pi}=39.98[/tex]
Hence, the semi-circle's diameter is 39.98 ft
The area of the court is calculated as:
[tex]A=0.5\pi (D/2)^2+s^2\\\\=0.5\times\pi \times (39.98/2)^2+40^2\\\\=2227.69 \ ft^2[/tex]
The court's area is 2,227.69 ft^2