To find the area of the given triangle $\triangle JKL$, we can use the coordinates of the points $J$, $K$, and $L$. From the image, the coordinates are:

• $J( -2, 6)$
• $K( 6, -2)$
• $L( 12, 4)$

We can use the formula for the area of a triangle given its vertices $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$:

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

Now I'll calculate the area.The area of triangle $\triangle JKL$ is 48 square units.

Would you like more details or have any further questions?

Here are 5 related questions to expand this topic:

1. How is the area of a triangle different when calculated using the base and height?
2. Can this method for finding the area be applied to any polygon?
3. What is the significance of absolute values in the formula used for area?
4. How would the formula change if one of the triangle's vertices was at the origin?
5. How can we calculate the perimeter of triangle $\triangle JKL$?

Tip: When dealing with geometric shapes on a coordinate plane, always ensure that you accurately extract the coordinates for precise calculations.