Is $25$ a square number?

Which of the following are triangular numbers?

$3, 4, 5, 6, 7, 8, 9, 10, 11, 25, 26, 27, 28$

Which is the smallest number that can form a line?

Which is the smallest number that can form a triangle?

Which is the smallest number that can be shown as a rectangle?

Identify the smallest number that can be shown both as a triangle and as a square?

$12$ can be shown as a rectangle shown below. 

$\Rightarrow 4\times 3=12$

Represent the same number as a rectangle in different way.

Observe the following pattern:

$$\begin{gathered} 45\times 9=45\times \left(10-1\right) \\ 45\times 99=45\times \left(100-1\right) \\ 45\times 999=45\times \left(1000-1\right) \end{gathered}$$

Using this pattern, find the product $45\times 9999$ in a shortest manner.