PSLE Figure 1 shows a triangular card RST with RT = TS. 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 36 pins were placed at an equal distance of 32 cm apart to hold the cards.
- Find the length of UV.
- Find the total area of the cards used.
(a)
Number of pins needed for the length of the board
= (36 - 2 x 2) ÷ 2
= (36 - 4) ÷ 2
= 32 ÷ 2
= 16
Number of pins is 1 more than the number of white triangles.
Number of white triangles to arrange lengthwise
= 16 - 1
= 15
Length of UV
= 15 x 32
= 480 cm
(b)
For lengthwise, the number of triangular cards is 1 less than the number of white triangles.
Number of triangular cards lengthwise
= 15 - 1
= 14
Number of triangular cards breadthwise = 3
Total number of triangular cards
= 14 + 14 + 3 + 3
= 34
Area of 1 triangular card
=
12 x 32 x 16
= 256 cm
2 Total area of 34 triangular cards
= 34 x 256
= 8704 cm
2 Answer(s): (a) 480 cm; (b) 8704 cm
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