The area of triagle OAB , the co-ordinates of whose vertices are A (4, 0) , B(0, 7) and O origin, is :

Options

A. 11 sq. units
B. 18 sq. units
C. 28 sq. units
D. 14 sq. units

Answer

To find the area of triangle OAB with vertices at A(4, 0), B(0, 7), and O(0, 0), we can use the formula for the area of a triangle formed by three points in a coordinate plane. The formula is:

\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]

### Step-by-step Solution:

1. **Identify the vertices of the triangle**:
- O (0, 0) is the origin.
- A (4, 0) is on the x-axis.
- B (0, 7) is on the y-axis.

2. **Determine the lengths of the base and height**:
- The base of the triangle can be taken as OA, which is the distance from O to A. Since A is at (4, 0), the length OA = 4 units.
- The height of the triangle can be taken as OB, which is the distance from O to B. Since B is at (0, 7), the length OB = 7 units.

3. **Apply the area formula**:
- Substitute the values of the base and height into the area formula:
\[ \text{Area} = \frac{1}{2} \times OA \times OB = \frac{1}{2} \times 4 \times 7 \]

4. **Calculate the area**:
- Calculate the multiplication:
\[ \text{Area} = \frac{1}{2} \times 28 = 14 \text{ square units} \]

5. **Conclusion**:
- The area of triangle OAB is 14 square units.