Find the area bounded by the line $x+y=10$ and both the co-ordinate axis.

Given: Line $x+y=10$.

To do: To find the area bounded by the line $x+y=10$ and both the co-ordinate axis.

As given, $x+y=10$

If $x=0\ \ \Rightarrow y=10$

If $x=10\ \ \Rightarrow y=0$

$\therefore$ The three points are $O( 0,\ 0),\ A( 10,\ 0)$ and $B( 0,\ 10)$

Using area formula

Area$=\frac{1}{2}[x_1( y_2-y_3)+x_2( y_3-y_1)+x_3( y_1-y_2)]$

$=\frac{1}{2}[0( 0-10)+10( 10-0)+0( 0−0)]$

$=\frac{1}{2}\times100=50\ sq.\ units$.