To find the area of the triangle shown in the image, we use the formula for the area of a triangle:

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

From the image:

• The base of the triangle is $(8x - 5)$ inches.
• The height of the triangle is $4x$ inches.

Plugging these values into the formula:

$\text{Area} = \frac{1}{2} \times (8x - 5) \times 4x$

Now let's simplify this expression:

$\text{Area} = \frac{1}{2} \times 4x \times (8x - 5)$

$\text{Area} = 2x \times (8x - 5)$

$\text{Area} = 2x \times 8x - 2x \times 5$

$\text{Area} = 16x^2 - 10x$

Thus, the area of the triangle is:

$\boxed{16x^2 - 10x} \text{ square inches}$

Would you like further details or have any other questions?

Here are some related questions you might consider:

1. How would the area change if the base and height were both doubled?
2. What are the dimensions of the triangle when $x = 2$?
3. How would you solve for $x$ if the area of the triangle were given?
4. How do you find the perimeter of the triangle given its side lengths?
5. What are some common errors to avoid when solving similar problems?

Tip: Always double-check your base and height measurements when using the area formula for triangles, as it's easy to mix up values.