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Fill in the blank! Leonardo’s triangle has an area of BLANK square units.

To find the area of triangle \(ABC\) given the vertices \(A(-5, -4)\), \(B(3, -3)\), and \(C(3, 2)\), we can use the formula for the area of a triangle with known vertices:

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

Here:
- \(A(x_1, y_1) = (-5, -4)\)
- \(B(x_2, y_2) = (3, -3)\)
- \(C(x_3, y_3) = (3, 2)\)

Substitute these coordinates into the formula:

\[
\text{Area} = \frac{1}{2} \left| (-5)((-3) - 2) + (3)(2 - (-4)) + (3)((-4) - (-3)) \right|
\]

Now, let's calculate step by step.

1. \((-3) - 2 = -5\)
2. \(2 - (-4) = 6\)
3. \((-4) - (-3) = -1\)

Substituting these values back into the formula:

\[
\text{Area} = \frac{1}{2} \left| (-5)(-5) + (3)(6) + (3)(-1) \right|
\]

Simplify the terms:

\[
\text{Area} = \frac{1}{2} \left| 25 + 18 - 3 \right|
\]
\[
\text{Area} = \frac{1}{2} \left| 40 \right|
\]
\[
\text{Area} = \frac{1}{2} \times 40 = 20
\]

So, the area of Leonardo's triangle is **20 square units**.

Would you like further details or have any questions?

Here are five relative questions:
1. How can the same formula be used for different triangles?
2. What happens if one of the points is at the origin?
3. Can you derive the formula for the area of a triangle from first principles?
4. What is the significance of the absolute value in the area formula?
5. How does the formula change for three-dimensional coordinates?

**Tip:** Always double-check your vertices' coordinates before applying the formula to avoid simple calculation errors.

Learn how to find the area of a triangle using vertices A(-5, -4), B(3, -3), and C(3, 2) in coordinate geometry. This tutorial walks through the step-by-step application of the area formula for triangles on a coordinate plane. Suitable for students in Grades 8-10.

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