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 5.
- How many squares were used to make a figure with an area of 180.5 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 5
= 5 x 5 ÷ 2
= 12.5 cm
2 (b)
Area of the figure = Figure number x Figure number ÷ 2
180.5 = Figure number x Figure number ÷ 2
180.5 x 2 = Figure number x Figure number
361 = Figure number x Figure number
Figure number = √361 = 19
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 19
= (19 - 1) x 19 ÷ 2
= 18 x 19 ÷ 2
= 171
Answer(s): (a) 12.5 cm
2; (b) 171