The continuous function $f(x)on$ the interval $-4,14$ has the values given $in$ the table below. The trapezoidal approximation for

${\displaystyle \underset{-4}{\overset{14}{}}}f(x)dx$ with $3$ subintervals $of$ equal length equals $162\mathrm{.}0.$ What $is$ the value $ofk?$

$(Answer$ accurate $to2$ decimal places.$)$