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

Concept: When we connect the midpoints of the four sides, another geometrical shape is formed that has the same properties as a parallelogram due to geometrical symmetry.

As a result, the new geometrical shape will be a parallelogram.

 $\Rightarrow LET PQRS$  is a rectangle.

$\Rightarrow$ Length of rectangle  $PQRS=8 cm$

$\Rightarrow$  Breadth of rectangle $PQRS=6cm$

$\Rightarrow$ Let  $A,B,C,D$ are the mid-points of the sides of rectangle $PQRS$, then $ABCD$  is a rhombus.

$\Rightarrow$ Then, diagonal of rhombus  $ABCD$ are $AC$ and $BD$.

$\Rightarrow$ Here,  $BD=QR=8 cm$ and  $AC=PQ=6 cm$

$\therefore Area of rhombus ABCD =\frac{Product of digonals}{2}$

$ABCD=\frac{8\times 6}{2}=4\times 6=24 c{m}^2$