PSLE Figure 1 shows a triangular card FGH with FH = HG. 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 26 pins were placed at an equal distance of 34 cm apart to hold the cards.
- Find the length of JK.
- Find the total area of the cards used.
(a)
Number of pins needed for the length of the board
= (26 - 1 x 2) ÷ 2
= (26 - 2) ÷ 2
= 24 ÷ 2
= 12
Number of pins is 1 more than the number of white triangles.
Number of white triangles to arrange lengthwise
= 12 - 1
= 11
Length of JK
= 11 x 34
= 374 cm
(b)
For lengthwise, the number of triangular cards is 1 less than the number of white triangles.
Number of triangular cards lengthwise
= 11 - 1
= 10
Number of triangular cards breadthwise = 2
Total number of triangular cards
= 10 + 10 + 2 + 2
= 24
Area of 1 triangular card
=
12 x 34 x 17
= 289 cm
2 Total area of 24 triangular cards
= 24 x 289
= 6936 cm
2 Answer(s): (a) 374 cm; (b) 6936 cm
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