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Answer 1 · 2017-07-23T08:21:11

The length is $=4.1cm$

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The length of the sides are

$AB=BC=CD=DA=6cm$

The angle

$hatA=hatC=40^@$

Therefore,

$hatB=hatD=180^@-40^@=140^@$

To calculate the longer diagonal, we apply the cosine rule to the triangle $DeltaACD$

$AC^2=AD^2+DC^2-2*AD*DC*cos hatD$

$AC^2=6^2+6^2-2*6*6*cos140^@$

$=36+36+72*(-0.766)$

$=72(1-0.766)=16.84$

Therefore,

$AC=sqrt16.84=4.1cm$