Fig. 12.26 depicts a racing track whose left and right ends are semicircular.
The distance between the two inner parallel line segments is 60 m and they are each 106 m long. If the track is 10 m wide, find:
(i) The distance around the track along its inner edge
(ii) The area of the track.
(i) Distance around the track along its inner edge = AB + arc BEC + CD + arc DFA
= 106 + 
* 2πr + 106 + 
* 2πr
= 212 + 
* 2 * 
* 30 + 
* 2 * 
* 30
= 212 + 2 * 
* 30
= 
= 
m
(ii) Area of the track = (Area of GHIJ - Area of ABCD) + (Area of semi-circle HKI - Area of semi-circle BEC) + (Area of semi-circle GLJ - Area of semi-circle AFD)
= 106 * 80 – 106 * 60 + 
* 
* (40)2 - 
* 
* (30)2 + 
* 
* (40)2 - 
* 
* (30)2
= 106 (80 – 60) + 
* (40)2 - 
* (30)2
= 106 (20) + 
[(40)2 – (30)2]
= 2120 + 
(40 – 30) (40 + 30)
= 2120 + (22/7) (10) (70)
= 2120 + 2200
= 4320 m2