The area of triangle formed with the origin and the points (4,0) and (0,6) is .........

Answer

To find the area of the triangle formed by the origin (0,0) and the points (4,0) and (0,6), we can follow these steps:

### Step 1: Identify the vertices of the triangle
The vertices of the triangle are:
- A (0,0) - the origin
- B (4,0) - on the x-axis
- C (0,6) - on the y-axis

### Step 2: Determine the base and height of the triangle
- The base of the triangle can be taken as the line segment from point A (0,0) to point B (4,0). The length of the base is:
\[ \text{Base} = 4 - 0 = 4 \text{ units} \]

- The height of the triangle can be taken as the vertical distance from point C (0,6) to the x-axis (line y=0). The height is:
\[ \text{Height} = 6 - 0 = 6 \text{ units} \]

### Step 3: Use the formula for the area of a triangle
The area \(A\) of a triangle can be calculated using the formula:
\[ A = \frac{1}{2} \times \text{Base} \times \text{Height} \]

### Step 4: Substitute the values of base and height into the formula
Substituting the values we found:
\[ A = \frac{1}{2} \times 4 \times 6 \]

### Step 5: Calculate the area
Calculating the area:
\[ A = \frac{1}{2} \times 24 = 12 \text{ square units} \]

### Final Answer
The area of the triangle formed by the origin and the points (4,0) and (0,6) is **12 square units**.

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