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.

NCERT Class 10 chapter 12

Page No. 236

Exercise 12.4

Question No. 8

# Figure depicts a racing track whose left and right ends are semicircular.

Share

(i)The distance around the track along its inner edge

= AB + arcBEC + CD + arcDFA

= 106 + 1/2 × 2πr + 106 + 1/2 × 2πr

= 106 + 1/2 × 2 × 22/7 × 30 + 106 + 1/2 × 2 × 22/7 × 30

= 212 + 2 × 22/7 × 30 = 212 + 1320/7 = 2804/7

(ii) Area of Track = (Area of GHIJ – Area of ABCD) + (Area of semicircle HKI – Area of semicircle BRC) + (Area of semicircle GLJ – Area of semicircle AFD)

= (106 × 80 – 106 × 60) + 1/2 × 22/7 × [(40)² – (30)²] + 1/2 × 22/7 × [(40)² – (30)²]

= 106(80 – 60) + 1/2 × 22/7 × (700) + 1/2 × 22/7 × (700) = 2120 + 22/7 × (700) = 2120 + 2200 = 4320