Area of Triangle Formed by Three Lines

Video Explanation

Question

Find the area of the triangle formed by the lines \(y = x\), \(x = 6\), and \(y = 0\).

Solution

Step 1: Find Points of Intersection

Intersection of \(y = x\) and \(y = 0\):

\[ x = 0 \Rightarrow (0,0) \]

Intersection of \(x = 6\) and \(y = 0\):

\[ (6,0) \]

Intersection of \(y = x\) and \(x = 6\):

\[ y = 6 \Rightarrow (6,6) \]

Step 2: Identify Triangle Vertices

\[ (0,0),\ (6,0),\ (6,6) \]

Step 3: Apply Area Formula

This is a right-angled triangle:

Base = 6, Height = 6

\[ \text{Area} = \frac{1}{2} \times 6 \times 6 \]

\[ = 18 \]

Final Answer

\[ \text{Area} = 18 \text{ sq. units} \]