To calculate the area of the triangle, we need to know the coordinates of its vertices.

From the image, the vertices of the triangle appear to be:

• $G$ at $(0, 2)$,
• $E$ at $(0, 0)$,
• $F$ at $(3, 0)$.

The area $A$ of a triangle with vertices at $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$ can be calculated using the formula:

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

Substituting the coordinates of $G(0, 2)$, $E(0, 0)$, and $F(3, 0)$:

$A = \frac{1}{2} \left| 0(0 - 0) + 0(0 - 2) + 3(2 - 0) \right|$ $A = \frac{1}{2} \times \left| 0 + 0 + 6 \right| = \frac{1}{2} \times 6 = 3$

Therefore, the area of the triangle is 3 square units.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. How do you find the area of a triangle using different methods, such as base and height?
2. What is the perimeter of this triangle based on the given vertices?
3. How can you verify if a triangle is a right triangle using its coordinates?
4. What happens to the area if the triangle is scaled by a factor of 2?
5. How would the area change if one vertex of the triangle moved along the x-axis?

Tip: Always double-check the coordinates on a graph to ensure precise calculations when solving geometry problems.