Answer:
The field inside a running track is made up of a rectangle 84.39 m long and 73 m wide, together with a half circle at each end. The running lanes are 9.76 wide all the way around. What is the area of the running track that goes around the field? Show your work.
Area of the running track is 4187.87 m^2
Step-by-step explanation:
Given:
Inner rectangle:
Length of the rectangle = 84.39 m
Width of the rectangle = 73 m
Radius of the inner semicircle = 36.5 m
Outer rectangle:
Length of the rectangle = (73+9.76+9.76) = 92.52 m
Width of the rectangle = 84.39 m
Radius of the outer semicircle = 46.26 m
We have to find the area of the running track.
Note:
Two semicircles with same radius makes a circle.
Area of the running track = ar (outer track) - ar (inner track)
Area of the track consist of one rectangle area along with 2 semicircles area (or a circles area).
⇒ Area of the running track :
⇒ ar (outer track) - ar (inner track)
⇒ [tex][ar\ \square_o + ar\ \bigcirc_o] - [ar\ \square_i + ar\ \bigcirc_i][/tex]
⇒ [tex][(92.52\times 84.39)+\pi (46.26)^2]-[(84.39\times 73)+\pi (36.5)^2][/tex]
⇒ [tex](7807.76+6722.96)- (6160.47+4185.38)[/tex]
⇒ [tex](14530.72)- (10345.85)[/tex]
⇒ [tex]4184.87\ m^2[/tex]
The area of the running track that goes around the field is 4187.87 m^2
