To calculate the area of the triangle in the provided graph, we will use the coordinates of the three points $I$, $H$, and $G$. Here are the steps:

1. Identify the coordinates:

   • $I$: (-10, 12)
   • $H$: (8, 8)
   • $G$: (2, 0)

2. Use the area formula for a triangle with vertices $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$: $\text{Area} = \frac{1}{2} \left| x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2) \right|$

3. Substitute the coordinates into the formula: $\text{Area} = \frac{1}{2} \left| -10(8-0) + 8(0-12) + 2(12-8) \right|$

   Simplify: $\text{Area} = \frac{1}{2} \left| -10(8) + 8(-12) + 2(4) \right|$ $\text{Area} = \frac{1}{2} \left| -80 - 96 + 8 \right|$ $\text{Area} = \frac{1}{2} \left| -168 \right|$ $\text{Area} = \frac{1}{2} \times 168 = 84 \text{ square units}$

4. Final Answer: The area of the triangle is 84 square units.

Let me know if you'd like additional explanations or have further questions.

Here are 5 related questions for exploration:

1. How does the triangle's area change if one vertex is moved vertically?
2. Can we find the area using a different method like dividing the triangle into right triangles?
3. How do coordinate-based area calculations compare to base-height approaches?
4. What happens to the area if all the coordinates are multiplied by 2?
5. How do you determine which triangle area formula applies based on given information?

Tip: Always double-check the coordinates to ensure calculations are precise when using graphs.