The track is 9.76 m wide all the way around. What is the distance around the outside of the track? Explain or show your reasoning.
Answers
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