PSLEThe figure shows a rectangular grass patch and an L-shaped footpath. The width of the footpath is 12 cm. The footpath is tiled using 68 circular tiles of diameter 6 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 3 x 3
= 28.26 cm
2 Area of a square plot that is under a circular tile
= 6 x 6
= 36 cm
2Area of the footpath not covered by a circular tile
= 36 - 28.26
= 7.74 cm
2 Area of the footpath not covered by all the tiles
= 7.74 x 68
= 526.32 cm
2 (b)
Number of circular tiles touching the 2 lengths of the grass patch
= (68 - 4) ÷ 2
= 64 ÷ 2
= 32
Perimeter of the grass patch
= 2 x 32 x 6
= 384 cm
Answer(s): (a) 526.32 cm
2; (b) 384 cm