Question

Area total e o volume da pirâmide da figura são,respectivamente iguais a:
a)964 e 72
b)1304 e 210
c)864 e 1296
d)1404 e 1296

Answer 1

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•$\sf c\acute alculo~do~ap\acute otema~da~base::\\\sf m=\dfrac{18}{2}=9~cm\\\sf c\acute alculo~do~ap\acute otema~da~pir\hat amide:\\\sf g^2=12^2+9^2\\\sf g^2=144+81\\\sf g^2=225\\\sf g=\sqrt{225}\\\sf g=15~cm$

•$\sf c\acute alculo~da~\acute area~lateral:\\\sf A_{\ell}=\diagup\!\!\!4\cdot\dfrac{18\cdot15}{\diagup\!\!\!2}=2\cdot18\cdot15=540~cm^2$

•$\sf c\acute alculo~da~\acute area~da~base:\\\sf A_b=18^2=324~cm^2$

Área total:

$\sf A_t= A_{\ell}+A_b\\\sf A_t=540+324\\\huge\boxed{\boxed{\boxed{\boxed{\sf A_t=864~cm^2}}}}$

Volume:

$\sf V=\dfrac{1}{3}\cdot A_b\cdot h\\\sf V=\dfrac{1}{\diagdown\!\!\! 3}\cdot324\cdot\diagdown\!\!\!\!\!\!12^4\\\huge\boxed{\boxed{\boxed{\boxed{\sf V=1296~cm^3}}}}$