Answer:
The area of triangle is 48.
Step-by-step explanation:
Given:
The vertices of triangle are (0,0),(12,0),(2,8).
Now, to find the area of triangle.
So, the coordinates of triangle are:
[tex]A(x_1,y_1)=(0,0)\:,\:B(x_2,y_2)=(12,0)\:and\:C(x_3,y_3)=(2,8)[/tex].
Now, to get the area of triangle we put formula:
[tex]Area\,of\,triangle\,=\,\frac{1}{2}\left|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\right|[/tex]
[tex]Area\,of\,triangle\,=\,\frac{1}{2}\left|0(0-8)+(12)(8-0)+2(0-0)\right|[/tex]
[tex]Area\,of\,triangle\,=\,\frac{1}{2}\left|0\times -8+12\times 8+2\times 0\right|[/tex]
[tex]Area\,of\,triangle\,=\,\frac{1}{2}\left|0+96+0\right|[/tex]
[tex]Area\,of\,triangle\,=\,\frac{1}{2}\left|96\right|[/tex]
[tex]Area\,of\,triangle\,=\,\frac{1}{2}\times 96[/tex]
[tex]Area\,of\,triangle\,=\,\frac{96}{2}[/tex]
[tex]Area\,of\,triangle\,=\,48.[/tex]
Therefore, the area of triangle is 48.
