PSLE Figure 1 shows a triangular card TUV with TV = VU. 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 36 cm apart to hold the cards.
- Find the length of WX.
- Find the total area of the cards used.
(a)
Number of pins needed for the length of the board
= (34 - 2 x 2) ÷ 2
= (34 - 4) ÷ 2
= 30 ÷ 2
= 15
Number of pins is 1 more than the number of white triangles.
Number of white triangles to arrange lengthwise
= 15 - 1
= 14
Length of WX
= 14 x 36
= 504 cm
(b)
For lengthwise, the number of triangular cards is 1 less than the number of white triangles.
Number of triangular cards lengthwise
= 14 - 1
= 13
Number of triangular cards breadthwise = 3
Total number of triangular cards
= 13 + 13 + 3 + 3
= 32
Area of 1 triangular card
=
12 x 36 x 18
= 324 cm
2 Total area of 32 triangular cards
= 32 x 324
= 10368 cm
2 Answer(s): (a) 504 cm; (b) 10368 cm
2