Henry Park Pri Sch 2007 PSLE Math Prelim Q41

In the following figures, the area of the biggest equilateral triangle is 64 square cm as shown in Figure 1. A new triangle is formed by connecting the midpoints of the sides of the previous triangle. If the pattern continues, find the area of the smallest triangle in Figure 4.



Solution

The shaded area of Figure 2 is ¼ of the Area of Figure 1 -----
¼ x 64 square cm = 16 square cm

The shaded area of Figure 3 is ¼ of the shaded area of Figure 2 -----
¼ x 16 square cm = 4 square cm

The shaded area of Figure 4 is ¼ of the shaded area of Figure 3 -----
¼ x 4 square cm = 1 square cm (Answer)