The area of a triangle with vertices A(3,0),B(7,0) and C(8,4) is

Options

A. `14`
B. `28`
C. `8`
D. `6`

Explanation

To find the area of the triangle with vertices A(3,0), B(7,0), and C(8,4), we can use the formula for the area of a triangle given its vertices:

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

Where:
- \( (x_1, y_1) = (3, 0) \) for point A
- \( (x_2, y_2) = (7, 0) \) for point B
- \( (x_3, y_3) = (8, 4) \) for point C

Now, we can substitute the coordinates into the formula step by step:

1. **Substituting the coordinates into the formula:**
\[ \text{Area} = \frac{1}{2} \left| 3(0 - 4) + 7(4 - 0) + 8(0 - 0) \right| \]

2. **Calculating each term inside the absolute value:**
- First term: \( 3(0 - 4) = 3 \times -4 = -12 \)
- Second term: \( 7(4 - 0) = 7 \times 4 = 28 \)
- Third term: \( 8(0 - 0) = 8 \times 0 = 0 \)

So, we have:
\[ \text{Area} = \frac{1}{2} \left| -12 + 28 + 0 \right| \]

3. **Combining the terms:**
\[ -12 + 28 + 0 = 16 \]

4. **Calculating the area:**
\[ \text{Area} = \frac{1}{2} \left| 16 \right| = \frac{1}{2} \times 16 = 8 \]

Thus, the area of the triangle is \( 8 \) square units.