Question

HELP PLEASE!!!!
The diagram shows an aerial view of a playground. What is the area of the playground to the nearest square yard?

Answer 1

@SithsAndGiggles can u help please?

Answer 2

The area of the playground will the be the area of the complete circle minus the shaded area, \(A_P=A_T-A_S\).

The total area would be \(A_T=\pi r^2=1225\pi\), since the radius is 35.

The sum of the area of the shaded region, \(A_S\), and the area of the triangle, \(A_\Delta\), is the area of the sector of this circle with arc measure \(360-280=80^\circ\). The area of the sector is is \(A_S+A_\Delta=\dfrac{80}{360}\pi r^2=\dfrac{2450\pi}{9}\).

The area of the triangle is \(A_\Delta=\dfrac{1}{2}(45)(25)=\dfrac{1125}{2}\), so \(A_S=\dfrac{2450\pi}{9}-\dfrac{1125}{2}\).

So, \(A_P=1225\pi-\dfrac{2450\pi}{9}+\dfrac{1125}{2}\approx3555.74\).