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.

Question

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.

KnowledgeBoat · Accepted Answer

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 = = 35 m. Area of both semi-circular parts = 2 × = πr² = = 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) = = 42 m. Circumference of both semi-circular part = πR + πR = 2πR. = = 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.

Mathematics

Mensuration

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