Question 945715
   
{{{Area = (p * q)/2}}} where {{{p}}} and {{{q}}} are the lengths of the diagonals.

side {{{s=8sqrt(3) ft}}}
longer diagonal is {{{p=24 ft }}}
first find the length of the shorter diagonal {{{q}}}

Use the Pythagorean theorem formula:

 {{{s^2 = (p/2)^2 + (q/2)^2}}}

{{{s= 8sqrt(3) }}}, {{{p/2=24ft/2=12ft}}}  

Therefore

{{{(8sqrt(3)ft)^2 = (12ft )^2 +  (q/2)^2}}}
{{{64*3ft^2 = 144ft ^2 +  (q/2)^2}}}
{{{192ft^2 -144ft ^2 = (q/2)^2}}}
{{{48ft ^2 =(q/2)^2}}}
{{{sqrt(48ft ^2 )=q/2}}}

{{{q=2*4sqrt(3)ft}}}

{{{q=8sqrt(3)ft}}} ...->the length of the shorter diagonal


{{{Area = (p * q)/2}}}

{{{Area = (24ft * 8sqrt(3)ft)/2}}}

{{{Area = (24ft * 4sqrt(3)ft)}}}

{{{Area = 96sqrt(3)ft^2}}}