We are given the area of a triangle, $A = 29.25 \, \text{square feet}$, and the height, $h = 6.5 \, \text{feet}$, and we are asked to find the length of the base, $b$.

The formula for the area of a triangle is:

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

Substituting the known values:

$29.25 = \frac{1}{2} \times b \times 6.5$

Now, we can solve for $b$.

First, multiply both sides by 2 to eliminate the fraction:

$2 \times 29.25 = b \times 6.5$

$58.5 = b \times 6.5$

Now, divide both sides by 6.5 to find $b$:

$b = \frac{58.5}{6.5}$

Let me calculate this value for you.The length of the base of the triangle is 9 feet.

Would you like more details or have any questions? Here are some related questions to explore:

1. How do you calculate the height of a triangle if the base and area are given?
2. What is the difference between the base and height in different types of triangles (e.g., right, equilateral)?
3. How does the formula for the area of a triangle change if you are given different units (e.g., inches or meters)?
4. How can you verify the area calculation if the base and height are known?
5. How would you find the perimeter of this triangle if the other sides were given?

Tip: Always remember that the height of a triangle is the perpendicular distance from the base to the opposite vertex.