Question

with the coordinates (10,6) , (0,3) ,(6,3) what is the area of the triangle in square units

Answer 1

To find the area of a triangle given its vertices, you can use the formula:

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

Let the vertices of the triangle be:
- \( A(10, 6) \) with coordinates \( (x_1, y_1) \)
- \( B(0, 3) \) with coordinates \( (x_2, y_2) \)
- \( C(6, 3) \) with coordinates \( (x_3, y_3) \)

Now, plug in the coordinates into the formula:

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

Calculating each term:

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

Now sum these results:

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

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