Question

Find the area of the triangle made by the line $x+y=4$ and the co-ordinate axes.

Answer 1

Given the equation of the line is $x+y=4.$

$x-$intercept of the equation will be,

$\begin{array}{cc}x+\left(0\right)& =4\\ x& =4\end{array}$

Hence, $x-$ intercept is $(4,0).$

$y-$intercept of the equation will be,

$\begin{array}{cc}\left(0\right)+y& =4\\ y& =4\end{array}$

Hence, $y-$ intercept is $(0,4).$

So, the area of the triangle will be,

$\begin{array}{cc}A& =\frac{1}{2}\times 4\times 4\\ & =2\times 4\\ & =8\text{sq. units}\end{array}$