Answer
$6.5$ meters
Work Step by Step
Comparing the two shadow lengths we can see that the flagpole's shadow ($9.1$ m) is bigger than the meter stick's shadow ($1.4$ m). But by how much?
Since $9.1 \div1.4 = 6.5$, it is also true that $1.4 \times 6.5 = 9.1$.
That means the flagpole's shadow is $6.5$ times longer than the meter stick's shadow. To make a shadow that is $6.5$ times longer, the flagpole itself must be $6.5$ times longer than the meter stick. The meter stick is $1$ meter long.
So, to find the flagpole length:
$$1\text{ m} \times 6.5 = 6.5 \text{ m}.$$
