Find the area of a triangle with vertices ( 0,4) , ( 0,2) and ( 3,0)

Answer

To find the area of a triangle with vertices at (0, 4), (0, 2), and (3, 0), we can use the formula for the area of a triangle given its vertices. The formula is:

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

Where the vertices are:
- \( (x_1, y_1) = (0, 4) \)
- \( (x_2, y_2) = (0, 2) \)
- \( (x_3, y_3) = (3, 0) \)

### Step 1: Substitute the coordinates into the formula

Substituting the coordinates into the area formula:

\[ \text{Area} = \frac{1}{2} \left| 0(2 - 0) + 0(0 - 4) + 3(4 - 2) \right| \]

### Step 2: Simplify the expression

Now, simplify the expression step by step:

1. Calculate \( 0(2 - 0) = 0 \)
2. Calculate \( 0(0 - 4) = 0 \)
3. Calculate \( 3(4 - 2) = 3 \times 2 = 6 \)

Putting it all together:

\[ \text{Area} = \frac{1}{2} \left| 0 + 0 + 6 \right| = \frac{1}{2} \left| 6 \right| = \frac{1}{2} \times 6 = 3 \]

### Step 3: Final Result

Thus, the area of the triangle is:

\[ \text{Area} = 3 \text{ square units} \]