Question

determinati aria totala a unei prisme hexagonale regulate cu aria bazei de
$54 \sqrt{3}$
si volumul de 324 cm

Answer 1

$Ab = 54 \sqrt{3} \: {cm}^{2}$

$Ab = \frac{3 {l}^{2} \sqrt{3} }{2}$

$\frac{3 {l}^{2} \sqrt{3} }{2} = 54 \sqrt{3}$

$3 {l}^{2} \sqrt{3} = 2 \times 54 \sqrt{3}$

$3 {l}^{2} \sqrt{3} = 108 \sqrt{3} \: | \div 3 \sqrt{3}$

${l}^{2} = 36$

$l = \sqrt{36}$

$l = 6 \: cm$

$Pb = 6l$

$Pb = 6 \times 6$

$Pb = 36 \: cm$

$V = 324 \: cm$

$V = Ab \times h$

$324 = 54 \sqrt{3} \times h$

$h = \frac{324}{54 \sqrt{3} }$

$h = \frac{6}{\sqrt{3}}$

$h=\frac{6\sqrt{3}}{3}$

$h=2\sqrt{3}\:cm$

$Al = Pb \times h$

$Al = 36 \times 2\sqrt{3}$

$Al = 72 \sqrt{3} \: {cm}^{2}$

$At = Al + 2Ab$

$At = 72 \sqrt{3} + 2 \times 54 \sqrt{3}$

$At = 72 \sqrt{3} + 108 \sqrt{3}$

$At = 180 \sqrt{3} \: {cm}^{2}$