PSLEThe figure shows a rectangular grass patch and an L-shaped footpath. The width of the footpath is 16 cm. The footpath is tiled using 60 circular tiles of diameter 8 cm, following the pattern shown. Each tile is in contact with those next to it.
- What is the area of the footpath not covered by the tiles? Take π = 3.14.
- What is the perimeter of the grass patch?
(a)
Area of a circular tile
= 3.14 x 4 x 4
= 50.24 cm
2 Area of a square plot that is under a circular tile
= 8 x 8
= 64 cm
2Area of the footpath not covered by a circular tile
= 64 - 50.24
= 13.76 cm
2 Area of the footpath not covered by all the tiles
= 13.76 x 60
= 825.6 cm
2 (b)
Number of circular tiles touching the 2 lengths of the grass patch
= (60 - 4) ÷ 2
= 56 ÷ 2
= 28
Perimeter of the grass patch
= 2 x 28 x 8
= 448 cm
Answer(s): (a) 825.6 cm
2; (b) 448 cm