Question

solve the problem using inductive reasoning.
how many triangles are in the next figure?

1 4 9

○ 16
○ 36
○ 12
○ 18

Explanation:

Step1: Identify pattern in counts

The number of triangles for each figure is:
Figure 1: $1 = 1^2$
Figure 2: $4 = 2^2$
Figure 3: $9 = 3^2$

Step2: Predict next figure's count

The next figure is the 4th one, so calculate $4^2$.
$4^2 = 16$

Answer:

A. 16