PSLE The figure shows a path of width 1 m in a rectangular park of length 14 m. The outline of the path is made up of quarter circles with centre E, semicircles with centre H and straight lines. EF = GH.
- 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 = 14 m
Length of 3 radii of the smaller circle
= 14 - 1 - 1
= 12 m
Radius of the smaller circles
= 12 ÷ 3
= 4 m
Width of the park
= 2 radii of the smaller circle + 2 widths of the path
= 2 x 4 + 2 x 1
= 10 m
(b)
Area of the path in one curve
= Area of the big quadrant - Area of the small quadrant
Radius of big quadrant
= 4 + 1
= 5 m
Area of the big quadrant
=
14 x 3.14 x 5 x 5
= 19.625 m
2 Area of the small quadrant
=
14 x 3.14 x 4 x 4
= 12.56 m
2 Area of the path in one curve
= 19.625 - 12.56
= 7.065 m
2 Total path = 3 curves + 1 rectangle
Area of the rectangle
= 1 x 5
= 5 m
2 Area of 3 curves
= 3 x 7.065
= 21.195 m
2 Area of the path
= 21.195 + 5
= 26.195 m
2 Answer(s): (a) 10 m; (b) 26.195 m
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