PSLE Figure 1 shows a triangular card MNP with MP = PN. 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 30 pins were placed at an equal distance of 36 cm apart to hold the cards.
- Find the length of QR.
- Find the total area of the cards used.
(a)
Number of pins needed for the length of the board
= (30 - 1 x 2) ÷ 2
= (30 - 2) ÷ 2
= 28 ÷ 2
= 14
Number of pins is 1 more than the number of white triangles.
Number of white triangles to arrange lengthwise
= 14 - 1
= 13
Length of QR
= 13 x 36
= 468 cm
(b)
For lengthwise, the number of triangular cards is 1 less than the number of white triangles.
Number of triangular cards lengthwise
= 13 - 1
= 12
Number of triangular cards breadthwise = 2
Total number of triangular cards
= 12 + 12 + 2 + 2
= 28
Area of 1 triangular card
=
12 x 36 x 18
= 324 cm
2 Total area of 28 triangular cards
= 28 x 324
= 9072 cm
2 Answer(s): (a) 468 cm; (b) 9072 cm
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