Question

The figure shows a running track surrounding a grassed enclosure PQRSTU. The enclosure consists of a rectangle PQST with a semicircular region at each end, PQ = 200 m; PT = 70 meters.

(i) Calculate the area of the grassed enclosure in m².
(ii) Given that the track is of constant width 7 m, calculate the outer perimeter ABCDEF of the track. (Take π = `22/7`)

Answer 1

(i) Area of the grassed enclosure
= PQ x PT + `2 xx 1/2` x π x (35)²   ...( ∵ r = `70/2` = 35 m)

= 200 x 70 + `22/7` x 35 m x 35 m
= 14000 + 22 x 5 x 35 m²
= [ 14000 + 110 x 35 ] m²
= 14000 + 3850 = 17850 m².

(ii) R = `[ (70 + 14)/2] "m" = 84/2 = 42 "m"`

Outer perimeter = 2I + 2 x `1/2` x 2πR
= 2 x 200 m + 2 x `22/7` x 42 m
= 400 m + 264 m
= 664 m.