PSLE The figure shows a path of width 5 m in a rectangular park of length 70 m. The outline of the path is made up of quarter circles with centre A, semicircles with centre D and straight lines. AB = CD.
- What is the width of the rectangular park?
- Find the area of the path. Take π = 3.14
(a)
Length of 3 radii of the smaller circle + 2 widths of the path = 70 m
Length of 3 radii of the smaller circle
= 70 - 5 - 5
= 60 m
Radius of the smaller circles
= 60 ÷ 3
= 20 m
Width of the park
= 2 radii of the smaller circle + 2 widths of the path
= 2 x 20 + 2 x 5
= 50 m
(b)
Area of the path in one curve
= Area of the big quadrant - Area of the small quadrant
Radius of big quadrant
= 20 + 5
= 25 m
Area of the big quadrant
=
14 x 3.14 x 25 x 25
= 490.625 m
2 Area of the small quadrant
=
14 x 3.14 x 20 x 20
= 314 m
2 Area of the path in one curve
= 490.625 - 314
= 176.625 m
2 Total path = 3 curves + 1 rectangle
Area of the rectangle
= 5 x 25
= 125 m
2 Area of 3 curves
= 3 x 176.625
= 529.875 m
2 Area of the path
= 529.875 + 125
= 654.875 m
2 Answer(s): (a) 50 m; (b) 654.875 m
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