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

The given lines

y = x, x = 6 and y = 0

.
Plot the graph of the line

y = x

using the table below:

So, the coordinates of the line equation

y = x

are

(0, 0)

and

(1, 1)

.
Plot the graph of the line

x = 6

using the table below:

So, the coordinates of the line equation

x = 6

are

(6, 0)

and

(6, 1)

.
Plot the graph of the line

y = 0

which is the x-axis.
The graph of the lines is represented as,

From the graph,
Height of the triangle

= 6 units

Base of the triangle

= 6 units

The area of the triangle,

A = \frac{1}{2} \times B \times H

\Rightarrow A = \frac{1}{2} \times 6 \times 6

\Rightarrow A = \frac{36}{2}

\Rightarrow A = 18

square units
Therefore, the area of the triangle formed by the lines

y = x, x = 6 and y = 0

is 18 square units.
Hence, option 3 is correct.

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