Triangle Area 443137

1. **State the problem:** We need to find the area of a triangle given its vertices on a coordinate grid. 2. **Identify the vertices:** From the description, the triangle's vertices are approximately at left-mid, upper-mid, and lower-right positions on the grid. Let's assign coordinates as follows: - Left-mid vertex: $A(0,2)$ - Upper-mid vertex: $B(2,4)$ - Lower-right vertex: $C(4,0)$ 3. **Formula for the area of a triangle given coordinates:** The area $A$ of a triangle with vertices $A(x_1,y_1)$, $B(x_2,y_2)$, and $C(x_3,y_3)$ is given by: $$ A = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| $$ 4. **Substitute the coordinates:** $$ A = \frac{1}{2} |0(4 - 0) + 2(0 - 2) + 4(2 - 4)| $$ 5. **Simplify inside the absolute value:** $$ = \frac{1}{2} |0 + 2 \times (-2) + 4 \times (-2)| = \frac{1}{2} |0 - 4 - 8| = \frac{1}{2} |-12| $$ 6. **Calculate the final area:** $$ = \frac{1}{2} \times 12 = 6 $$ **Answer:** The area of the triangle is $6$ units².