PSLE Figure 1 shows a triangular card EFG with EG = GF. 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 24 pins were placed at an equal distance of 52 cm apart to hold the cards.
- Find the length of HJ.
- Find the total area of the cards used.
(a)
Number of pins needed for the length of the board
= (24 - 1 x 2) ÷ 2
= (24 - 2) ÷ 2
= 22 ÷ 2
= 11
Number of pins is 1 more than the number of white triangles.
Number of white triangles to arrange lengthwise
= 11 - 1
= 10
Length of HJ
= 10 x 52
= 520 cm
(b)
For lengthwise, the number of triangular cards is 1 less than the number of white triangles.
Number of triangular cards lengthwise
= 10 - 1
= 9
Number of triangular cards breadthwise = 2
Total number of triangular cards
= 9 + 9 + 2 + 2
= 22
Area of 1 triangular card
=
12 x 52 x 26
= 676 cm
2 Total area of 22 triangular cards
= 22 x 676
= 14872 cm
2 Answer(s): (a) 520 cm; (b) 14872 cm
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