Let's recheck the calculations to ensure the correct area of the triangle.

### Recalculation of the Area

Given vertices:
- \((6, 0)\) from Line 1 (intersection with the \(x\)-axis)
- \((1, 0)\) from Line 2 (intersection with the \(x\)-axis)
- \((3, 2)\) from the intersection of both lines

The formula for the area of a triangle formed by three points \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\) is:

\[
\text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right|
\]

Substituting the given vertices:

\[
\text{Area} = \frac{1}{2} \left| 6(0 - 2) + 1(2 - 0) + 3(0 - 0) \right|
\]
\[
= \frac{1}{2} \left| 6(-2) + 2 + 0 \right|
\]
\[
= \frac{1}{2} \left| -12 + 2 \right|
\]
\[
= \frac{1}{2} \times 10 = \frac{10}{2} = 5 \text{ square units}
\]

### Re-Verification of the Calculation

The calculation indicates that the area is 5 square units. If your result is 3 square units, let's review possible sources of discrepancy:

1. **Vertices:** Ensure the correct coordinates of the vertices are used.
2. **Formula:** Verify the correct application of the area formula.
3. **Intersection Points:** Double-check the intersection points of the lines.

If you provide the steps or approach that gave you 3 square units, I can help identify where the difference might have arisen. Would you like to explore that further?

Explore the recalculation of the area of a triangle formed by given vertices using the area formula. Learn how to apply the formula correctly and re-verify calculations to ensure accuracy. Suitable for Grades 9-12.

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