1-cm square tiles and triangular tiles were used to make some figures. The area of each triangular tile was half that of a square tile. The first four figures are shown.
- Find the area of Figure 8.
- How many squares were used to make a figure with an area of 312.5 cm2?
(a)
Pattern for the area of the figure
Figure 1 = 1 x 1 ÷ 2 = 0.5 cm
2 Figure 2 = 2 x 2 ÷ 2 = 2 cm
2 Figure 3 = 3 x 3 ÷ 2 = 4.5 cm
2 Figure 4 = 4 x 4 ÷ 2 = 8 cm
2 Formula:
Area of the figure = Figure number x Figure number ÷ 2
Area of Figure 8
= 8 x 8 ÷ 2
= 32 cm
2 (b)
Area of the figure = Figure number x Figure number ÷ 2
312.5 = Figure number x Figure number ÷ 2
312.5 x 2 = Figure number x Figure number
625 = Figure number x Figure number
Figure number = √625 = 25
Pattern for number of squares
Figure 1 = 0
Figure 2 = 0 + 1
Figure 3 = 0 + 1 + 2
Figure 4 = 0 + 1 + 2 + 3
Formula:
Number of squares = (Figure Number - 1) x Figure Number ÷ 2
Number of squares at Figure 25
= (25 - 1) x 25 ÷ 2
= 24 x 25 ÷ 2
= 300
Answer(s): (a) 32 cm
2; (b) 300