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Fig. 12.26 depicts a racing track whose ...

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.

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We are given the following information:
(i) A racing track whose right and left ends are semicircular.
(ii) The distance between the 2 inner parallel line segments is `60` m and they are `106` m long.
(iii) Width of track = `10` m
Radii of the inner semicircles HIJ and KLG `(r_1) = 60/2 = 30 m`
Radii of the outer semicircles BCD and EFA = `30 m + 10 m = 40` m
JK = GH = `106` m
DJ = HB = `10` m
(i) The distance around the track along its inner edge.
= GH + arc HIJ + JK + arc KLG
= `106 + 2 pi r_1r/2 + 106 + 2pi r_1/2`
= `106 + pi × 30 + 106 + pi × 30`
= `212 + 1320/7`
= `(1484 + 1320)/7`
= `2804/7 m`
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