To solve this problem, we use the formula for the area of a triangle:

$A = \frac{1}{2} \cdot b \cdot h$

Where:

• $b$ is the base of the triangle.
• $h$ is the height of the triangle.

From the image:

• The base ($b$) is labeled as $6x + 7$.
• The height ($h$) is labeled as $4x + 2$.

Step 1: Multiply the base and the height.

$b \cdot h = (6x + 7)(4x + 2)$

Using distributive property: $(6x + 7)(4x + 2) = 24x^2 + 12x + 28x + 14 = 24x^2 + 40x + 14$

Step 2: Apply the formula for the area.

$A = \frac{1}{2} \cdot (24x^2 + 40x + 14)$

Distribute the $\frac{1}{2}$: $A = 12x^2 + 20x + 7$

Final Answer:

The area of the patch is: $A = 12x^2 + 20x + 7$

Matching the Correct Values:

The terms to move to the boxes are:

1. $12x^2$
2. $20x$
3. $7$

Let me know if you'd like further clarification or details! Here are some related questions for practice:

1. What is the distributive property, and how is it used in algebra?
2. Why do we divide by $2$ when calculating the area of a triangle?
3. How do you simplify algebraic expressions with multiple terms?
4. What are the rules for multiplying polynomials?
5. How can this formula be applied to triangles of different orientations?

Tip: Always check that the units or variables in an equation are consistent before solving.