Question

What is the area of the triangle in square units? A(0,3), B(10,6), C(6,3)

Answer 1

To find the area of the triangle formed by the points \( A(0, 3) \), \( B(10, 6) \), and \( C(6, 3) \), we can use the formula for the area of a triangle given its vertices \( (x_1, y_1) \), \( (x_2, y_2) \), and \( (x_3, y_3) \):

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

Here, we have:
- \( A(0, 3) \): \( (x_1, y_1) = (0, 3) \)
- \( B(10, 6) \): \( (x_2, y_2) = (10, 6) \)
- \( C(6, 3) \): \( (x_3, y_3) = (6, 3) \)

Now we substitute these coordinates into the formula:

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

Calculating each term:

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

Putting it all together:

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

Thus, the area of the triangle is

\[
\boxed{9} \text{ square units.}
\]