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

$\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}$

Given:

• Base = $12x$ cm
• Height = $3.4x$ cm

Substitute these values into the formula:

$\text{Area} = \frac{1}{2} \times 12x \times 3.4x$

Now, simplify the expression:

$\text{Area} = \frac{1}{2} \times (12 \times 3.4) \times x^2$ $\text{Area} = \frac{1}{2} \times 40.8 \times x^2$ $\text{Area} = 20.4x^2 \, \text{cm}^2$

Thus, the area of the triangle is $20.4x^2$ square centimeters.

Would you like more details on how I arrived at this answer, or do you have any other questions?

Here are 5 related questions you might find interesting:

1. How does changing the height affect the area of the triangle?
2. What would the area be if $x = 2$?
3. How would you calculate the area of a triangle if you only knew the three sides?
4. What other formulas can be used to find the area of triangles with given information?
5. How do units of area change when multiplying by a variable like $x^2$?

Tip: Always double-check that you’re using the correct units when calculating area, especially if they involve variables or unknowns!