The figure obtained by joining the mid-points of adjacent sides of rectangle of sides 8cm and 6cm is

PQRS is a parallelogram and adjacent sides are equal. So PQRS is a rhombus.

$\therefore AreaofPQRS=4\frac{1}{2}\times OP\times OS$

                                    $=4\times \frac{1}{2}\times 3\times 4$

                                    $=24c{m}^2$