PSLE Figure 1 shows a triangular card BCD with BD = DC. 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 54 cm apart to hold the cards.
- Find the length of EF.
- Find the total area of the cards used.
(a)
Number of pins needed for the length of the board
= (34 - 1 x 2) ÷ 2
= (34 - 2) ÷ 2
= 32 ÷ 2
= 16
Number of pins is 1 more than the number of white triangles.
Number of white triangles to arrange lengthwise
= 16 - 1
= 15
Length of EF
= 15 x 54
= 810 cm
(b)
For lengthwise, the number of triangular cards is 1 less than the number of white triangles.
Number of triangular cards lengthwise
= 15 - 1
= 14
Number of triangular cards breadthwise = 2
Total number of triangular cards
= 14 + 14 + 2 + 2
= 32
Area of 1 triangular card
=
12 x 54 x 27
= 729 cm
2 Total area of 32 triangular cards
= 32 x 729
= 23328 cm
2 Answer(s): (a) 810 cm; (b) 23328 cm
2