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.

1. Find the area of Figure 9.
2. How many squares were used to make a figure with an area of 200 cm²?

(a)
Pattern for the area of the figure
Figure 1 = 1 x 1 ÷ 2 = 0.5 cm²
Figure 2 = 2 x 2 ÷ 2 = 2 cm²
Figure 3 = 3 x 3 ÷ 2 = 4.5 cm²
Figure 4 = 4 x 4 ÷ 2 = 8 cm²

Formula:
Area of the figure = Figure number x Figure number ÷ 2

Area of Figure 9
= 9 x 9 ÷ 2
= 40.5 cm²

(b)
Area of the figure = Figure number x Figure number ÷ 2
200 = Figure number x Figure number ÷ 2
200 x 2 = Figure number x Figure number
400 = Figure number x Figure number

Figure number = √400 = 20

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 20
= (20 - 1) x 20 ÷ 2
= 19 x 20 ÷ 2
= 190

Answer(s): (a) 40.5 cm²; (b) 190