Answer
$4.5\sqrt6$
Work Step by Step
$u=(1,3,5)-(3,3,0)=(-2,0,5)$
$v=(-2,0,5)-(3,3,0)=(-5,-3,5)$
are two sides of the triangle.
We know that for a matrix
$
\left[\begin{array}{rrr}
a & b & c \\
d &e & f \\
g &h & i \\
\end{array} \right]
$
the determinant, $D=a(ei-fh)-b(di-fg)+c(dh-eg).$
$u×v$ is the determinant of the matrix $\begin{bmatrix}
i& j & k \\
-2& 0&5\\
-5&-3 &5 \\
\end{bmatrix}
$
Thus $u×v=(15,-15,6).$
Thus $A=0.5|u\times v|=0.5\sqrt{15^2+(-15)^2+6^2}=0.5\sqrt{486}=4.5\sqrt6$
