Find area of the triangle with vertices at the point given in each of the following: (i) $(1,0),(6,0),(4,3)$ (ii) $(2,7),(1,1),(10,8)$
Find area of the triangle with vertices at the point given in each of the following: (i) $(1,0),(6,0),(4,3)$ (ii) $(2,7),(1,1),(10,8)$

Formula for Area of triangle:

$\frac{1}{2}\left|\begin{array}{lll}x_{1} & y_{1} & 1 \\ x_{2} & y_{2} & 1 \\ x_{3} & y_{3} & 1\end{array}\right|$

(i)

$\frac{1}{2}\left|\begin{array}{lll}1 & 0 & 1 \\ 6 & 0 & 1 \\ 4 & 3 & 1\end{array}\right|$

$=\frac{15}{2}$ sq. units

(ii) Area $=\frac{1}{2}\left|\begin{array}{lll}2 & 7 & 1 \\ 1 & 1 & 1 \\ 10 & 8 & 1\end{array}\right|$

$=\frac{1}{2}[2(1-8)-7(1-10)+1(8-10)]$

$=\frac{47}{2}$ sq. unit