PSLE The figure shows a path of width 1 m in a rectangular park of length 11 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 = 11 m
Length of 3 radii of the smaller circle
= 11 - 1 - 1
= 9 m
Radius of the smaller circles
= 9 ÷ 3
= 3 m
Width of the park
= 2 radii of the smaller circle + 2 widths of the path
= 2 x 3 + 2 x 1
= 8 m
(b)
Area of the path in one curve
= Area of the big quadrant - Area of the small quadrant
Radius of big quadrant
= 3 + 1
= 4 m
Area of the big quadrant
=
14 x 3.14 x 4 x 4
= 12.56 m
2 Area of the small quadrant
=
14 x 3.14 x 3 x 3
= 7.065 m
2 Area of the path in one curve
= 12.56 - 7.065
= 5.495 m
2 Total path = 3 curves + 1 rectangle
Area of the rectangle
= 1 x 4
= 4 m
2 Area of 3 curves
= 3 x 5.495
= 16.485 m
2 Area of the path
= 16.485 + 4
= 20.485 m
2 Answer(s): (a) 8 m; (b) 20.485 m
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