A plane makes intercepts OA, OB and OC whose measurements are D and c on the OX, OY and OZ axes. The area of triangle ABC is

 Plane meets axes at A(a, 0, 0), B(0, b, 0) and C(0, 0, c). 

Then area of $∆ABC$

$\begin{array}{l}=\frac{1}{2}|\overrightarrow{\mathrm{AB}}\times \overrightarrow{\mathrm{AC}}|\\ =\frac{1}{2}\left|\right(-\mathrm{a}\widehat{\mathrm{i}}+\widehat{\mathrm{bj}})\times (-\mathrm{a}\widehat{\mathrm{i}}+\mathrm{c}\widehat{\mathrm{k}}\left)\right|\\ =\frac{1}{2}\sqrt{\left({\mathrm{a}}^2{\mathrm{b}}^2+{\mathrm{b}}^2{\mathrm{c}}^2+{\mathrm{c}}^2{\mathrm{a}}^2\right)}\end{array}$