PSLE Figure 1 shows a triangular card UVW with UW = WV. A number of such cards were arranged along the four sides of a rectangular board. Figure 2 shows part of the arrangement. A total of 32 pins were placed at an equal distance of 32 cm apart to hold the cards.
- Find the length of XY.
- Find the total area of the cards used.
(a)
Number of pins needed for the length of the board
= (32 - 2 x 3) ÷ 2
= (32 - 6) ÷ 2
= 26 ÷ 2
= 13
Number of pins is 1 more than the number of white triangles.
Number of white triangles to arrange lengthwise
= 13 - 1
= 12
Length of XY
= 12 x 32
= 384 cm
(b)
For lengthwise, the number of triangular cards is 1 less than the number of white triangles.
Number of triangular cards lengthwise
= 12 - 1
= 11
Number of triangular cards breadthwise = 4
Total number of triangular cards
= 11 + 11 + 4 + 4
= 30
Area of 1 triangular card
=
12 x 32 x 16
= 256 cm
2 Total area of 30 triangular cards
= 30 x 256
= 7680 cm
2 Answer(s): (a) 384 cm; (b) 7680 cm
2