What is the slant height x of this square pyramid? Express your answer in radical form.

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Answer 1 · 2017-05-24T04:45:23

Slant height is #3.464# meters.

Consider the triangular face, which appears as follows:
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It is apparent that while side #AB=4# meters, #/_B=/_C=60^@#

Hence #/_a=180^@-60^@-60^@=60^@# and #DeltaABC# is an equilateral triangle.

and slant height #AD=x#, where #AD_|_BC#

Nowin #DeltasACD# and #ABD#, we have #AB=AC#, #/_B=/_C# and #AD=AD# and from #SSS# postulate we have #DeltaACD-=DeltaABD#

and hence #CD=BD# and as #BC=4# meters and hence #CD=BD=2# meters.

Now, we have from Pythagoras theorem

#AB^2=AD^2+BD^2#

i.e. #4^2=AD^2+2^2#

or #16=AD^2+4#

i.e. #AD=12#

and #AD=sqrt12=3.464# meters

Hence, slant height is #3.464# meters.