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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#