The vertices of a triangle are (1, 0), (4, 0) and (4, 4). Its area is :

Options

A. 4 sq. units
B. 6 sq. units
C. 8 sq. units
D. None of these

Answer

To find the area of the triangle with vertices at (1, 0), (4, 0), and (4, 4), we can follow these steps:

### Step 1: Identify the vertices
The vertices of the triangle are given as:
- A(1, 0)
- B(4, 0)
- C(4, 4)

### Step 2: Determine the base and height
In this triangle:
- The base can be taken as the horizontal line segment AB, which lies along the x-axis from point A(1, 0) to point B(4, 0).
- The height is the vertical distance from point C(4, 4) down to the line segment AB (the x-axis).

### Step 3: Calculate the length of the base
The length of the base AB can be calculated as:
\[ \text{Base} = |x_B - x_A| = |4 - 1| = 3 \]

### Step 4: Calculate the height
The height is the y-coordinate of point C since it is the vertical distance from point C to the x-axis:
\[ \text{Height} = y_C = 4 \]

### Step 5: Use the area formula for 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 6: Substitute the values into the formula
Substituting the values of the base and height into the area formula:
\[ A = \frac{1}{2} \times 3 \times 4 \]

### Step 7: Calculate the area
Now, calculate the area:
\[ A = \frac{1}{2} \times 3 \times 4 = \frac{12}{2} = 6 \]

### Final Answer
The area of the triangle is \( 6 \) square units.

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