Question

The area of a triangle whose vertices are $A(3,2),B(11,8)$ and $C(8,12)$ is

• A. $20$ sq.units
• B. $25$ sq.units
• C. $35$ sq.units
• D. $15$ sq.units

Answer 1

The correct option is B $25$ sq.units

The area of the given triangle is $A=\frac{1}{2}\left|\begin{array}{ccc}3& 2& 1\\ 11& 8& 1\\ 8& 12& 1\end{array}\right|$
Operating $R_1\to R_1-R_2$ and $R_2\to R_2-R_3$
$\Rightarrow A=\frac{1}{2}\left|\begin{array}{ccc}-8& -6& 0\\ 3& -4& 0\\ 8& 12& 1\end{array}\right|$
Expanding through $C_3,$ we get
$A=\frac{1}{2}\left|\begin{array}{cc}-8& -6\\ 3& -4\end{array}\right|=25$ sq.units