PSLE Figure 1 shows a triangular card DEF with DF = FE. 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 28 pins were placed at an equal distance of 52 cm apart to hold the cards.
- Find the length of GH.
- Find the total area of the cards used.
(a)
Number of pins needed for the length of the board
= (28 - 1 x 2) ÷ 2
= (28 - 2) ÷ 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 GH
= 12 x 52
= 624 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 = 2
Total number of triangular cards
= 11 + 11 + 2 + 2
= 26
Area of 1 triangular card
=
12 x 52 x 26
= 676 cm
2 Total area of 26 triangular cards
= 26 x 676
= 17576 cm
2 Answer(s): (a) 624 cm; (b) 17576 cm
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