Question

As arestas laterais de uma pirâmide reta medem 15 cm e a sua base é um quadrado cujos lados medem 18 cm .
Determine : Me ajuda por favor

A) A altura dessa pirâmide
B) A área da superfície (total)
C) O volume​

Answer 1

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$\tt a)~\sf 15^2= g^2+\left(\dfrac{18}{2}\right)^2\\\sf 225=g^2+81\\\sf g^2=225-81\\\sf g^2=144\\\sf g=\sqrt{144}\\\sf g=12~cm\\\sf m=\dfrac{18}{2}=9\\\sf g^2=m^2+h^2\\\sf 144=9^2+h^2\\\sf h^2+81=144\\\sf h^2=144-81\\\sf h^2=63\\\sf h=\sqrt{63}\\\huge\boxed{\boxed{\boxed{\boxed{\boxed{\sf h=7\sqrt{3}~cm\checkmark}}}}}$

$\tt b)~\sf c\acute alculo~da~\acute area~lateral: \\\sf A_l=\diagup\!\!\!\!4^2\cdot\dfrac{1}{\diagup\!\!\!\!2}\cdot 18\cdot12\\\sf A_l=2\cdot18\cdot12\\\sf A_l=432~cm^2\\\sf c\acute alculo~da~\acute area~da~base:\\\sf B=18^2=324~cm^2\\\sf A_{tota\ell}=A_l+B\\\sf A_{tota\ell}=432+324\\\huge\boxed{\boxed{\boxed{\boxed{\sf A_{tota\ell}=756~cm^2\checkmark}}}}$

$\sf V=\dfrac{1}{3}\cdot B\cdot h\\\sf V=\dfrac{1}{\backslash\!\!\!3}\cdot \diagup\!\!\!\!\!32\diagup\!\!\!4^{108}\cdot7\sqrt{3}\\\sf V=108\cdot7\sqrt{3}\\\huge\boxed{\boxed{\boxed{\boxed{\boxed{\sf V=756\sqrt{3}~cm^3\checkmark}}}}}$