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 34 pins were placed at an equal distance of 30 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
= (34 - 2 x 3) ÷ 2
= (34 - 6) ÷ 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 30
= 390 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 = 4
Total number of triangular cards
= 12 + 12 + 4 + 4
= 32
Area of 1 triangular card
=
12 x 30 x 15
= 225 cm
2 Total area of 32 triangular cards
= 32 x 225
= 7200 cm
2 Answer(s): (a) 390 cm; (b) 7200 cm
2