\magnification=\magstep1

$$
{ {\Delta L} \over {L} } \quad = \quad {{\rm 1\ cm}\over{\rm 10\ cm}}
              \quad = \quad 0.1 \quad = \quad 10\%
$$

$$
{ {\Delta w} \over {w} } \quad = \quad {{\rm 1\ cm}\over{\rm 5\ cm}}
              \quad = \quad 0.2 \quad = \quad 20\%
$$

$$
A \quad = \quad L \thinspace w \quad = \quad 
           ({\rm 10\ cm}) \thinspace ({\rm 5\ cm})  \quad = \quad
           {\rm 50\ cm^2}
$$

$$
{ {\Delta A}\over{A} } \quad = \quad
       {{\Delta L}\over{L}} \thinspace + \thinspace  
                      {{\Delta w}\over{w}} \quad = \quad
       { 10\% \thinspace + \thinspace 20\% } \quad = \quad 30\%
$$

$$
{\Delta A} \quad = \quad (A) \thinspace \left( {{\Delta A}\over{A}} \right) 
                             \quad = \quad
                    ({\rm 50\ cm^2}) \thinspace (30\%) \quad = \quad
                     {\rm 15\ cm^2} 
$$

$$
{A} \quad = \quad {\rm 50\ cm^2} \thinspace \pm \thinspace {\rm 15\ cm^2}
$$

\bye

