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We are given the coordinates of points \( D(-2, 8) \), \( E(2, 0) \), and \( F(-2, -4) \), and we need to find the area of triangle \( \Delta DEF \).

The formula for the area of a triangle given its vertices \( (x_1, y_1) \), \( (x_2, y_2) \), and \( (x_3, y_3) \) is:

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

Substituting the coordinates \( D(-2, 8) \), \( E(2, 0) \), and \( F(-2, -4) \) into this formula, we get:

\[
\text{Area} = \frac{1}{2} \left| (-2)(0 - (-4)) + 2((-4) - 8) + (-2)(8 - 0) \right|
\]

Let me calculate that for you.The area of triangle \( \Delta DEF \) is \( 24 \) square units.

Do you want further details or have any questions?

Here are some related questions for practice:
1. What is the perimeter of triangle \( \Delta DEF \)?
2. Can you find the centroid (center of mass) of triangle \( \Delta DEF \)?
3. How would the area change if point \( D \) was shifted to \( (-3, 8) \)?
4. What is the slope of line \( DE \) in \( \Delta DEF \)?
5. How can you use the distance formula to calculate the lengths of the sides of \( \Delta DEF \)?

**Tip:** When working with triangles on a coordinate plane, the formula for the area becomes much simpler when you know the vertices!

What is the area of triangle DEF with points D(-2, 8), E(2, 0), and F(-2, -4)?

Find the area of triangle DEF with vertices D(-2, 8), E(2, 0), and F(-2, -4) using the coordinate geometry formula. This solution is suitable for students in Grades 8-10.

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