PSLE The figure shows a path of width 5 m in a rectangular park of length 55 m. The outline of the path is made up of quarter circles with centre B, semicircles with centre E and straight lines. BC = DE.
- 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 = 55 m
Length of 3 radii of the smaller circle
= 55 - 5 - 5
= 45 m
Radius of the smaller circles
= 45 ÷ 3
= 15 m
Width of the park
= 2 radii of the smaller circle + 2 widths of the path
= 2 x 15 + 2 x 5
= 40 m
(b)
Area of the path in one curve
= Area of the big quadrant - Area of the small quadrant
Radius of big quadrant
= 15 + 5
= 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 15 x 15
= 176.625 m
2 Area of the path in one curve
= 314 - 176.625
= 137.375 m
2 Total path = 3 curves + 1 rectangle
Area of the rectangle
= 5 x 20
= 100 m
2 Area of 3 curves
= 3 x 137.375
= 412.125 m
2 Area of the path
= 412.125 + 100
= 512.125 m
2 Answer(s): (a) 40 m; (b) 512.125 m
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