Question 1160635

<a href="https://www.imageupload.net/image/c8KqW"><img src="https://imagehost.imageupload.net/2020/06/06/rhombus.th.png" alt="rhombus.png" border="0" /></a>




The sides of a rhombus are all congruent. (the same length).

{{{AB=BC=CD=DA}}}

The two diagonals are perpendicular, and they bisect each other. This means they cut each other in half.

{{{AO=OC=(1/2)AC}}}, and {{{BO=OD=(1/2)BD}}}

if he perimeter of the rhombus is {{{20dm}}}  , then  

{{{4AB=20dm}}}
{{{AB=5dm}}}

since {{{AB=5dm}}}, and if its longer diagonal is {{{AC=8dm}}}=> {{{(1/2) AC=4dm}}}, then {{{1/2 }}}of shorter diagonal is 

{{{(OB)^2=(AB)^2-((1/2)AC)^2}}}..... substitute values from above

{{{(OB)^2=(5dm)^2-(4dm)^2}}}

{{{(OB)^2=25dm^2-16dm^2}}}

{{{(OB)^2=9dm^2}}}

{{{OB=3dm}}}->{{{1/2 }}}of shorter diagonal, so the length of its shorter diagonal {{{BD=6dm}}}

and its area will be: 
You can find the area in square units of the rhombus by multiplying the lengths of the two diagonals   and dividing by two

in your case the length of diagonals is {{{8dm}}} and {{{6dm}}}, so we have

{{{A=(8dm*6dm)/2}}}

{{{A=48dm^2/2}}}

{{{A=24dm^2}}}