To solve for the area of the triangle shown:

The area of a triangle is given by:

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

Information provided:

• Base = $(6x - 1)$ inches
• Height = $8x$ inches

Substituting values into the formula:

$\text{Area} = \frac{1}{2} \times (6x - 1) \times 8x$

Simplify:

$\text{Area} = 4x \times (6x - 1)$ $\text{Area} = 24x^2 - 4x \, \text{(square inches)}$

Thus, the area of the triangle is $24x^2 - 4x$ square inches.

Would you like to:

1. Evaluate the area for a specific $x$?
2. Go over step-by-step simplification?
3. Discuss similar problems with variable expressions in geometry?
4. Explore how to validate the dimensions of such problems?
5. Learn how to solve related triangle problems using the Pythagorean theorem?

Tip: Always double-check your substitutions and algebra when solving problems with variables!