Question

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

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

Leonardo's triangle has an area of __ square units

Answer 1

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

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

Plugging in the coordinates for points A, B, and C:

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

We can now substitute these values into the formula:

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

Calculating each term step by step:

1. Calculate \(-5(-3-2)\):
\[
-5(-5) = 25
\]

2. Calculate \(3(2 - (-4))\):
\[
3(2 + 4) = 3 \times 6 = 18
\]

3. Calculate \(3(-4 - (-3))\):
\[
3(-4 + 3) = 3(-1) = -3
\]

Now we sum these results:

\[
25 + 18 - 3 = 40
\]

Now substitute this back into the area formula:

\[
\text{Area} = \frac{1}{2} |40| = \frac{40}{2} = 20
\]

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