PSLE The figure shows a path of width 4 m in a rectangular park of length 62 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 = 62 m
Length of 3 radii of the smaller circle
= 62 - 4 - 4
= 54 m
Radius of the smaller circles
= 54 ÷ 3
= 18 m
Width of the park
= 2 radii of the smaller circle + 2 widths of the path
= 2 x 18 + 2 x 4
= 44 m
(b)
Area of the path in one curve
= Area of the big quadrant - Area of the small quadrant
Radius of big quadrant
= 18 + 4
= 22 m
Area of the big quadrant
=
14 x 3.14 x 22 x 22
= 379.94 m
2 Area of the small quadrant
=
14 x 3.14 x 18 x 18
= 254.34 m
2 Area of the path in one curve
= 379.94 - 254.34
= 125.6 m
2 Total path = 3 curves + 1 rectangle
Area of the rectangle
= 4 x 22
= 88 m
2 Area of 3 curves
= 3 x 125.6
= 376.8 m
2 Area of the path
= 376.8 + 88
= 464.8 m
2 Answer(s): (a) 44 m; (b) 464.8 m
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