To find the area of a triangle, you use the formula:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

Given the base is $\frac{2}{9}$ and the height is $\frac{7}{9}$, the area is calculated as follows:

$\text{Area} = \frac{1}{2} \times \frac{2}{9} \times \frac{7}{9}$

First, multiply the fractions:

$\frac{2}{9} \times \frac{7}{9} = \frac{2 \times 7}{9 \times 9} = \frac{14}{81}$

Now, multiply by $\frac{1}{2}$:

$\text{Area} = \frac{1}{2} \times \frac{14}{81} = \frac{14}{162}$

Finally, simplify the fraction if possible. The greatest common divisor (GCD) of 14 and 162 is 2, so:

$\frac{14}{162} = \frac{7}{81}$

Thus, the area of the triangle is $\frac{7}{81}$.

Would you like more details or have any questions?

Here are 5 related questions to consider:

1. How do you simplify complex fractions?
2. What is the formula for the area of a triangle when given different types of measurements?
3. How do you find the area of a triangle with non-fractional dimensions?
4. How does changing the base or height affect the area of a triangle?
5. Can you find the area of other shapes using similar methods?

Tip: When dealing with fractions in geometric formulas, it helps to simplify the fractions at each step to avoid large numbers and make calculations easier.