https://file.aiquickdraw.com/mathbot/file/17270998451321fmjqww1.jpg

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.

Learn how to find the area of a triangle using coordinate geometry. This problem uses the formula for calculating the area of a triangle with known vertices: G(0, 2), E(0, 0), and F(3, 0). Suitable for students in Grades 7-9.

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