Remark
It is really hard to tell what the playground is. Is he running around 45 yards plus the circumference of part of the circle? Or is just the triangle? Since pi is mentioned, I'll take it to be 45 + part of the circumference, but the ambiguity makes it possible to be wrong.
Equation
Distance = 2* (280/360) * pi * r + 45
Givens
r = 35 yards
Solve
C = 2 * 3.14 * (280/360) * 35 + 45
C = 2 * 3.14 * (0.77777777) * 35 + 45
C = 6.28 * 35 * 0.777777 + 45
C = 170.9555556
Answer
C = the distance for 1 lap around the playground. David went around 3 times.
3*C = 3 * 170.95555556
3C = 512.8666667
The distance he went is 513 yards <<<< Answer