PSLE The figure shows a path of width 2 m in a rectangular park of length 28 m. The outline of the path is made up of quarter circles with centre R, semicircles with centre U and straight lines. RS = TU.
- 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 = 28 m
Length of 3 radii of the smaller circle
= 28 - 2 - 2
= 24 m
Radius of the smaller circles
= 24 ÷ 3
= 8 m
Width of the park
= 2 radii of the smaller circle + 2 widths of the path
= 2 x 8 + 2 x 2
= 20 m
(b)
Area of the path in one curve
= Area of the big quadrant - Area of the small quadrant
Radius of big quadrant
= 8 + 2
= 10 m
Area of the big quadrant
=
14 x 3.14 x 10 x 10
= 78.5 m
2 Area of the small quadrant
=
14 x 3.14 x 8 x 8
= 50.24 m
2 Area of the path in one curve
= 78.5 - 50.24
= 28.26 m
2 Total path = 3 curves + 1 rectangle
Area of the rectangle
= 2 x 10
= 20 m
2 Area of 3 curves
= 3 x 28.26
= 84.78 m
2 Area of the path
= 84.78 + 20
= 104.78 m
2 Answer(s): (a) 20 m; (b) 104.78 m
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