The figure (i) given below 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 m.

(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.

Given,

PQ = 200 m and PT = 70 m.

(i) By formula,

Area of rectangle PQST = l × b

= 200 × 70

= 14000 m².

Radius of each semi-circular part on either side of rectangle = $\dfrac{PT}{2} = \dfrac{70}{2}$ = 35 m.

Area of both semi-circular parts = 2 × $\dfrac{πr^2}{2}$ = πr²

= $\dfrac{22}{7} \times 35 \times 35$

= 22 × 5 × 35

= 3850 m².

So, the total area of grassed enclosure = 14000 + 3850 = 17850 m².

Hence, area of glassed enclosure = 17850 m².

(ii) Given,

Width of track around the enclosure = 7 m.

From figure,

AB = PQ = 200 m

ED = ST = 200 m

EA = PT + ET + AP = 70 + 7 + 7 = 84 m

BD = DS + QS + BQ = 70 + 7 + 7 = 84 m

Outer radius of semi-circle (R) = $\dfrac{EA}{2} = \dfrac{84}{2}$ = 42 m.

Circumference of both semi-circular part = πR + πR = 2πR.

= $2 \times \dfrac{22}{7} \times 42$

= 264 m.

From figure,

Outer perimeter = Circumference of both semi-circular part + ED + AB

= 264 + 200 + 200

= 664 m.

Hence, perimeter of outer track ABCDEF = 664 m.