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 H, semicircles with centre L and straight lines. HJ = KL.

1. What is the width of the rectangular park?
2. 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 m²

Area of the small quadrant
= ¹₄ x 3.14 x 18 x 18
= 254.34 m²

Area of the path in one curve
= 379.94 - 254.34
= 125.6 m²

Total path = 3 curves + 1 rectangle

Area of the rectangle
= 4 x 22
= 88 m²

Area of 3 curves
= 3 x 125.6
= 376.8 m²

Area of the path
= 376.8 + 88
= 464.8 m²

Answer(s): (a) 44 m; (b) 464.8 m²