Question

Leonardo draws the obtuse triangle pictured here and calculates the area in square units. What is the area of Leonardo's triangle?

Point A: (-5, -4)
Point B: (3, -3)
Point C: (3, 2)

Answer 1

To find the area of triangle ABC with vertices A (-5, -4), B (3, -3), and C (3, 2), we can use the formula for the area of a triangle given its vertices \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\):

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

Substituting in the coordinates of points A, B, and C:

- \( (x_1, y_1) = (-5, -4) \)
- \( (x_2, y_2) = (3, -3) \)
- \( (x_3, y_3) = (3, 2) \)

Calculating the individual terms:

1. \( x_1(y_2 - y_3) = -5(-3 - 2) = -5(-5) = 25 \)
2. \( x_2(y_3 - y_1) = 3(2 - (-4)) = 3(2 + 4) = 3(6) = 18 \)
3. \( x_3(y_1 - y_2) = 3(-4 - (-3)) = 3(-4 + 3) = 3(-1) = -3 \)

Now, summing these up:

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

Thus, the area of Leonardo's triangle is:

\[
\boxed{20} \text{ square units}
\]