A stadium is in circular shape. Within the stadium some areas have been allotted for a hockey court and a javelin range, as given in the figure. Assume the shape of the hockey court and the javelin range to be square and triangle, resp. The curators would like to accommodate a few more sports in the stadium. Help them by measuring the unallocated region within the stadium.(the radius of the stadium is 200 mts.)
We need to find the unallocated area within the stadium.
The unallocated area should be = The total circular area of the stadium – Area of the hockey court - Area of the Javelin Range.
The area of circular stadium =π×r2
The area of hockey court (square), we know that the radius of the stadium forms the diagonal of the hockey court.
Therefore the sides of the hockey court will be a =r√2, (applying Pythagoras Theorem in a square)
Then, the area of the square =a2
= 20000 m2
Javelin Range is a right angled triangle
area of the right triangle = 12×r×r
Therefore the unallocated area in the stadium =Total area of stadium – Area of the hockey court – Area of the Javelin Range
The unallocated area within the stadium is 40000(π−1) m2.