To find the area of the triangle, we will use the formula for the area of a triangle with vertices $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$:

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

From the graph, the coordinates of the vertices appear to be:

• $I(-12, 8)$
• $H(8, 8)$
• $G(4, 2)$

Substitute these values into the formula:

$\text{Area} = \frac{1}{2} \left| (-12)(8 - 2) + 8(2 - 8) + 4(8 - 8) \right|$

Simplify:

$\text{Area} = \frac{1}{2} \left| (-12)(6) + 8(-6) + 4(0) \right|$

$\text{Area} = \frac{1}{2} \left| -72 - 48 + 0 \right|$

$\text{Area} = \frac{1}{2} \left| -120 \right|$

$\text{Area} = \frac{1}{2} \cdot 120 = 60$

Thus, the area of the triangle is:

$\boxed{60 \text{ square units}}$

Let me know if you have any questions or need further assistance!

Questions to Explore:

1. How does the coordinate geometry formula for area compare with using base and height directly?
2. Can this method be extended to polygons with more than three sides?
3. How would you handle the problem if one or more points were not integer values?
4. What other properties of the triangle can be calculated (e.g., side lengths, angles)?
5. How can we verify the calculation using another method?

Tip:

When working with graphs, always double-check coordinates to ensure accuracy in calculations!