Answer
Find out the area of the running track that goes around the field .
To proof
Formula
Area of rectangle = length× breadth
[tex]Area\ of\ semi-circle = \frac{1}{2}\pi r^{2}[/tex]
[tex]\pi =3.14[/tex]
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
[tex]= \frac{92.52}{2}[/tex]
=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
[tex]= \frac{73}{2}[/tex]
=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
