Question

Leonardo draws the obtuse triangle pictured here and calculates the area in square units. What is the area of Leonardo’s triangle? (1 point) Leonardo’s triangle has an area of square units.
a(-5,-4)
b(3,-3)
c(3,2)

Answer 1

To calculate the area of the triangle formed by the points \( A(-5, -4) \), \( B(3, -3) \), and \( C(3, 2) \), we can use the formula for the area of a triangle given by its vertices:

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

where \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\) are the coordinates of the vertices.

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

Substituting the points into the area formula:

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

Calculating each term step by step:

1. \( -5(-3 - 2) = -5(-5) = 25 \)
2. \( 3(2 - (-4)) = 3(2 + 4) = 3 \times 6 = 18 \)
3. \( 3((-4) - (-3)) = 3(-4 + 3) = 3(-1) = -3 \)

Putting it all together:

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

Thus, the area of Leonardo's triangle is \( \boxed{20} \) square units.