PSLE The figure shows a path of width 2 m in a rectangular park of length 22 m. The outline of the path is made up of quarter circles with centre Q, semicircles with centre T and straight lines. QR = ST.
- 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 = 22 m
Length of 3 radii of the smaller circle
= 22 - 2 - 2
= 18 m
Radius of the smaller circles
= 18 ÷ 3
= 6 m
Width of the park
= 2 radii of the smaller circle + 2 widths of the path
= 2 x 6 + 2 x 2
= 16 m
(b)
Area of the path in one curve
= Area of the big quadrant - Area of the small quadrant
Radius of big quadrant
= 6 + 2
= 8 m
Area of the big quadrant
=
14 x 3.14 x 8 x 8
= 50.24 m
2 Area of the small quadrant
=
14 x 3.14 x 6 x 6
= 28.26 m
2 Area of the path in one curve
= 50.24 - 28.26
= 21.98 m
2 Total path = 3 curves + 1 rectangle
Area of the rectangle
= 2 x 8
= 16 m
2 Area of 3 curves
= 3 x 21.98
= 65.94 m
2 Area of the path
= 65.94 + 16
= 81.94 m
2 Answer(s): (a) 16 m; (b) 81.94 m
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