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

### Step 1: Assign the coordinates
Assign the coordinates of the points:
- \( x_1 = 3, y_1 = 0 \)
- \( x_2 = 7, y_2 = 0 \)
- \( x_3 = 8, y_3 = 4 \)

### Step 2: Plug the values into the formula
Substituting the values into the area formula:

\[ \text{Area} = \frac{1}{2} \left| 3(0 - 4) + 7(4 - 0) + 8(0 - 0) \right| \]

### Step 3: Calculate each term
Calculate each term inside the absolute value:

1. \( 3(0 - 4) = 3 \times -4 = -12 \)
2. \( 7(4 - 0) = 7 \times 4 = 28 \)
3. \( 8(0 - 0) = 8 \times 0 = 0 \)

Now, substitute these values back into the area formula:

\[ \text{Area} = \frac{1}{2} \left| -12 + 28 + 0 \right| \]

### Step 4: Simplify the expression
Now simplify the expression inside the absolute value:

\[ -12 + 28 + 0 = 16 \]

### Step 5: Calculate the final area
Now calculate the area:

\[ \text{Area} = \frac{1}{2} \left| 16 \right| = \frac{16}{2} = 8 \]

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

### Final Answer
The area of the triangle with vertices A(3,0), B(7,0), and C(8,4) is \( 8 \) square units.

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