Question

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

Answer 1

To find the area of the triangle with vertices at 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 \((x_3, y_3)\):

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

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

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

Now plug in the coordinates:

\[
\text{Area} = \frac{1}{2} \left| 0(6 - 3) + 10(3 - 3) + 6(3 - 6) \right|
\]
\[
= \frac{1}{2} \left| 0 + 0 + 6(-3) \right|
\]
\[
= \frac{1}{2} \left| -18 \right|
\]
\[
= \frac{1}{2} \times 18
\]
\[
= 9
\]

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