There are a few key things to consider in this word problem. The first is that the shape of the playground is a square, so the sides are the same length, or 109 yards long.

We can find the area of a square by multiplying the length times the width, so the area of the total playground is 109*109 or 109^{2}.

The next statement is that the there is a skating rink in each corner that is formed of a quadrant of a circle. This means that if you took a circle and cut into four equal wedges and put those wedges in the corner, this would be our skating rinks. We can find the area of the total circle, which the formula is A=π*r^{2}

They gave us the area of the remaining playground area 9055 square yards(I am going to assume square yards but if not, you need to convert units).

We take our answer 109^{2} square yards for the whole playground and subtract the 9055 square yards. This will give you the area of the circle for the skating rinks. We plug in this number into the area of a circle formula (A=π*r^{2}) and solve for r. We ignore any negative answers because distance is positive.

The cost of cementing the skating rinks is found by multiplying the $2.50 times the area of the circle found above.

I will leave the computations to you, but I hope that this helps!

Jose M.

thank you so much. you are going to make an excellent teacher.10/13/19