The area of a triangle with vertices A (0,8), O(0,0) and B (5,0) is

Options

A. 8 sq. unite
B. 13 sq. units
C. 20 sq. units
D. 40 sq. units

Answer

To find the area of the triangle with vertices A(0, 8), O(0, 0), and B(5, 0), we can use the formula for the area of a triangle given its vertices at coordinates (x1, y1), (x2, y2), and (x3, y3):

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

### Step-by-Step Solution:

1. **Identify the coordinates of the vertices:**
- A (0, 8) → (x1, y1) = (0, 8)
- O (0, 0) → (x2, y2) = (0, 0)
- B (5, 0) → (x3, y3) = (5, 0)

2. **Substitute the coordinates into the area formula:**
\[ \text{Area} = \frac{1}{2} \left| 0(0 - 0) + 0(0 - 8) + 5(8 - 0) \right| \]

3. **Calculate each term:**
- The first term: \(0(0 - 0) = 0\)
- The second term: \(0(0 - 8) = 0\)
- The third term: \(5(8 - 0) = 40\)

4. **Combine the terms:**
\[ \text{Area} = \frac{1}{2} \left| 0 + 0 + 40 \right| = \frac{1}{2} \left| 40 \right| = \frac{1}{2} \times 40 = 20 \]

5. **Final Result:**
The area of the triangle is \(20\) square units.