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.)
Answers
Given : areas allotted for a 'HOCKEY COURT' and a 'JAVELIN RANGE', as shown in the figure
Radius of stadium = 200 m
To Find : (A) The area ( in sq. m) allotted to javelin range' is:
(B) If the team of the curators managing the stadium, likes to allot space for some more sports, how much area (in sq. m) is available to them?
(C) If the boundaries of the hockey court and javelin range are to be fenced, then the total length ( in m) of the fence required is:
(D) Whose area is larger?
Solution:
Two perpendicular sides of triangle are radius
Hence Area of triangle = (1/2) * 200 x 200
= 20000 m²
The area ( in sq. m) allotted to javelin range' is: 20000
Diagonal of Square = Radius
Area of Square = (1/2)* 200² = 20000 m² ( area of square = (1/2) diagnoal²)
Area of Hockey ground = 20000 m²
Both Areas are Equal
Area of circle = πR² = 3.14 x 200² = 125600 m²
Remaining Area = 125600 - 20000 - 20000
= 85600 m²
Hypotenuse of Triangle = 200√2
Side of square = 200/√2
Fence required = 200 + 200 + 200√2 + 4(200/√2)
= 400 + 600√2
= 1248.52 m
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