Question

Um poliedro convexo tem 4 faces hexagonais e 4 faces triangulares. Determine a quantidade de vértices e arestas desse poliedro.

Answer 1

$\mathrm{Sendo\ k\ o\ n\acute{u}mero\ de\ faces\ com\ forma\ de\ um}\\ \mathrm{poligono\ de\ n\ lados:}\\\\ \mathrm{A=\dfrac{1}{2}\sum{k_in_i}\ \to\ A=\dfrac{k_1n_1+k_2n_2}{2}\ \to}\\\\ \mathrm{\to\ A=\dfrac{4.6+4.3}{2}=12+6=18\ \to\ \boxed{\mathrm{A=18}}}\\\\ \mathrm{F=k_1+k_2=4+4\ \to\ \boxed{\mathrm{F=8}}}\\\\ \mathrm{V+F=A+2\ \to V+8=18+2\ \to\ \boxed{\mathrm{V=12}}}$