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? explain your reasoning.

Answer

Find out the  area of the running track that goes around the field .

To proof

Formula

Area of rectangle = length× breadth

area of running track = outside area - inside area

First case ( outside )

length = 73 + 2 × 9.76

          = 92.52m

Breadth = 84.39 m

radius of outside semi circle

=46.26m

outside area = area of rectangle + 2× area of the semi- circle

                     =  92.52× 84.39  + 3.14× 46.26 ×46.26

                     =  7807.76+ 6719.56

                     = 14527.32 m² ( approx)

Second case

radius of the semi- circle

=36.5m

inside area =  area of rectangle + 2× area of the semi- circle

                  = 73× 84.39 +  3.14×  36.5 ×36.5

                  = 6160.47 + 4183.27

                  = 10343.74m²

area of running track=   14527.32 m² - 10343.74m²

                     = 4183.58m²

Hence proved