PSLE The figure shows a path of width 4 m in a rectangular park of length 56 m. The outline of the path is made up of quarter circles with centre V, semicircles with centre Y and straight lines. VW = XY.
- 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 = 56 m
Length of 3 radii of the smaller circle
= 56 - 4 - 4
= 48 m
Radius of the smaller circles
= 48 ÷ 3
= 16 m
Width of the park
= 2 radii of the smaller circle + 2 widths of the path
= 2 x 16 + 2 x 4
= 40 m
(b)
Area of the path in one curve
= Area of the big quadrant - Area of the small quadrant
Radius of big quadrant
= 16 + 4
= 20 m
Area of the big quadrant
=
14 x 3.14 x 20 x 20
= 314 m
2 Area of the small quadrant
=
14 x 3.14 x 16 x 16
= 200.96 m
2 Area of the path in one curve
= 314 - 200.96
= 113.04 m
2 Total path = 3 curves + 1 rectangle
Area of the rectangle
= 4 x 20
= 80 m
2 Area of 3 curves
= 3 x 113.04
= 339.12 m
2 Area of the path
= 339.12 + 80
= 419.12 m
2 Answer(s): (a) 40 m; (b) 419.12 m
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