There is a rectangular park of length 55 m and breadth 42 m in a JNV. It has small flower beds in the shape of Trapezium, Square, Triangle and circle in it as shown in the figure. The dimensions of these flower beds are also given. Vidyalaya has planted Variety of flowers in these flower beds to beautify it. The figure is given below
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Answer:
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Step-by-step explanation:
rectangular park is surrounded by 4 semicircular flower beds.
so the diameter of two semicircles =100m
diameter of another two semicircles=50m
the area of semicircles= area of two big semicircles+ area of two small semicircles
=2πr²+2πR²
=2(22/7 ×50×50)+2(22/7 ×25×25)
=2×22/7(50×50+25×25)
=44/7(2500+625)
=44/7(3125)
=44×3125/7=19642.8 approx
cost=19642.8×60/100
=11785 rupees.
Answer i) :-
→ Area of ∆ = (1/2) * Base * height = (1/2) * 2 * 3.5 = 3.5 m².
→ Area of square = (side)² = (2.5)² = 6.25 m².
therefore, Square bed has more area than triangle.
Answer ii) :-
→ Area of circle = πr² = (22/7) * 2.1 * 2.1 = 22 * 0.3 * 2.1 = 13.86m².
→ Area of trapezium = (1/2)(sum of parallel sides) * height = (1/2) * (2 + 3) * 1.5 = (1/2) * 5 * 1.5 = 2.5 * 1.5 = 3.75 m².
since ,
→ 3.5 < 3.75 < 6.25 < 13.86 .
→ ∆ < trapezium < square < circle .
therefore, triangular flower bed has least area.
Answer iii) :-
→ Perimeter of vidyalaya park = 2(L + B) = 2(55 + 42) = 2 * 97 = 194 m (Ans.)
Answer iv) :-
→ Cost of planting Jasmine flower in circular flower bed = Rate / m² * Area of circular flower bed = 8 * 13.86 = Rs.110.88 (Ans.)
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