PSLEThe figure shows a rectangular grass patch and an L-shaped footpath. The width of the footpath is 20 cm. The footpath is tiled using 56 circular tiles of diameter 10 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 5 x 5
= 78.5 cm
2 Area of a square plot that is under a circular tile
= 10 x 10
= 100 cm
2Area of the footpath not covered by a circular tile
= 100 - 78.5
= 21.5 cm
2 Area of the footpath not covered by all the tiles
= 21.5 x 56
= 1204 cm
2 (b)
Number of circular tiles touching the 2 lengths of the grass patch
= (56 - 4) ÷ 2
= 52 ÷ 2
= 26
Perimeter of the grass patch
= 2 x 26 x 10
= 520 cm
Answer(s): (a) 1204 cm
2; (b) 520 cm