Area of the triangle whose base is given by $\overline{A}=i+j+k$ and one of the two sides by$\overline{B}=4j+3k$                         

$\overline{B}=4j+3k$

$\overrightarrow{A}\times \overrightarrow{B}=\left|\begin{array}{ccc}i& j& k\\ 1& 1& 1\\ 0& 4& 3\end{array}\right|$

$=i\left(3-4\right)-j\left(3-0\right)+k\left(4-0\right)$

$=-\hat{i}-3\hat{j}+4\hat{k}$

$\left|\overrightarrow{A}\times \overrightarrow{B}\right|=\sqrt{1^2+3^2+4^2}=\sqrt{26}$

$\frac{1}{2}\left|\overrightarrow{A}\times \overrightarrow{B}\right|=\frac{1}{2}\sqrt{26}$

$=\frac{\sqrt{26}}{2}$