Question

what is the area of the triangle in square units?
The three corners are: (0,3), (6,3), and (10,6)

Answer 1

To find the area of a triangle given its vertices at points \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\), we can use the formula:

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

Given the vertices of the triangle:

- \((x_1, y_1) = (0, 3)\)
- \((x_2, y_2) = (6, 3)\)
- \((x_3, y_3) = (10, 6)\)

We can plug these values into the formula:

\[
\text{Area} = \frac{1}{2} \left| 0(3 - 6) + 6(6 - 3) + 10(3 - 3) \right|
\]

Breaking down the calculations:

1. \(0(3 - 6) = 0\)
2. \(6(6 - 3) = 6 \cdot 3 = 18\)
3. \(10(3 - 3) = 10 \cdot 0 = 0\)

Now, substitute these into the area formula:

\[
\text{Area} = \frac{1}{2} \left| 0 + 18 + 0 \right| = \frac{1}{2} \left| 18 \right| = \frac{18}{2} = 9
\]

Thus, the area of the triangle is \(\boxed{9}\) square units.